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If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expan

by levemi 10y ago

If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expanded if it was always infinite in size. I'm not even sure the concept of expansion even makes sense. What is infinite + 1? It's just infinite. It seems more like the expansion is a distribution of internal things.

stouset 10y ago
Take the set of positive integers (0, 1, 2…). Double them, so you have (0, 2, 4…). You had an infinite list of numbers, all "compact" (no room for more positive integers inbetween them), and with a simple mathematical transform, you've given yourself space for a second equally-sized infinity of integers to fit neatly inside of them.
DonaldFisk 10y ago
You can see back as far as the Big Bang, approximately 14 billion years ago, so all matter in the visible Universe is within 14 billion light years of the Earth. However, the space the Universe occupies is only really finite if it's positively curved. If it's flat or negatively curved, the space it occupies is infinite, and if its density is constant, it must contain an infinite amount of matter even though we only see part of it. The Big Bang is a singularity - a point with infinite density. It's hard to get your head around intuitively, but it all makes sense mathematically. (The maths is pretty hard, and rarely covered at undergraduate level.) The simplest model in rough agreement with observations is called the Einstein-de Sitter Model, and it's flat with a zero cosmological constant. See http://www.britannica.com/science/cosmology-astronomy/Relativistic-cosmologies#ref1069808 http://www.britannica.com/science/cosmology-astronomy/Relati... More general models are covered here: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Solutions https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...
- dsfuoi 10y ago
  Radius of the visible universe is actually 45.7 billion ly.
  - DonaldFisk 10y ago
    Thanks for the correction: https://en.wikipedia.org/wiki/Observable_universe https://en.wikipedia.org/wiki/Observable_universe
DougWebb 10y ago
Off the cuff thought: the overall universe is infinite and not expanding, and it's only the visible universe that's expanding into that infinite space. Now try to wrap your mind around this: someone that's one light year to the left is going to see a slightly different visible universe, also expanding, into the same infinite space. But if we look in their direction, we see the edge of our visible universe expanding into the void, but from their point of view looking in the same direction our edge is one light year short of their edge. So what's our edge expanding into?
- Razengan 10y ago
  I've always wondered; is there a "last" galaxy in any direction, such that for an observer in that galaxy, no further light or radiation can be detected from that direction? (outside that galaxy) That, must be a terrifying place to live in......
  - hellameta 10y ago
    I don't see how our situation is any less terrifying haha
    - Razengan 10y ago
      It's certainly less terrifying than having to look at an infinite abyss.
      - hellameta 10y ago
        I really enjoy your belief that you're somehow not always looking at an infinite abyss :P
  - Razengan 10y ago
    Too late to edit, but I must add that I'm not necessarily asking if there's an "edge" of the Universe.
    - deleted 10y ago
Retric 10y ago
Math includes the idea of orders of infinity. There are infinite prime numbers, there are more positive integers, even more integers (positive and negative), even more rational numbers (A/B), and even more numbers (rational + irrational {e, Pi} etc)...
- pcmonk 10y ago
  In what sense are there more rational numbers than prime numbers? They can be put into bijection with each other, so we generally think of them as being same infinity. There are more real nubmers, of course, by Cantor's diagonalization, so your basic point is true.
  - Retric 10y ago
    The set of all prime numbers is contained within the set of rational numbers, but they are rational numbers that are not within the set of prime numbers. Cantor's diagonalization is simply demonstrating that same inequality by showing a number in set A is not in set B. Just because you can map two infinity's to each other does not mean they are of the same size consider: Limit(0->inifinity) of (x - (x/2)) algebraically that's clearly Limit(0->inifinity) of X/2 which is infinity. PS: What makes Cantor's diagonalization interesting is you can repeat it recursively an infinite number of times. This is more obvious in base 2.
    - JBiserkov 10y ago
      >Cantor's diagonalization is simply demonstrating that same inequality by showing a number in set A is not in set B. If that were true, why go to all the trouble, just show 1/2 which is not a natural number, or sqrt(2) which is not a rational number. Cantor's diagonalization is proving that no mapping exists between the natural numbers and the real numbers in [0, 1]; that no matter what mapping you (try to) come up, there will be a number you would miss. The primes and rationals have the same size (cardinality) as the natural numbers, namely countably infinite. See https://en.wikipedia.org/wiki/Countable_set#Formal_overview_without_details https://en.wikipedia.org/wiki/Countable_set#Formal_overview_...
gnodar 10y ago
I don't know the answer to your question, but I can imagine how something can expand if it's infinite. Imagine an infinitelylong rubber band in front of you. Now imagine grabbing it with two hands and pulling them away from each other, causing the rubber band to stretch. If you take a sharpie, and paint dots on a spot representing planets or whatever else, they will pull away from eachother as you stretch the rubber band.

by levemi 10y ago

stouset 10y ago

Take the set of positive integers (0, 1, 2…). Double them, so you have (0, 2, 4…). You had an infinite list of numbers, all "compact" (no room for more positive integers inbetween them), and with a simple mathematical transform, you've given yourself space for a second equally-sized infinity of integers to fit neatly inside of them.

DonaldFisk 10y ago

You can see back as far as the Big Bang, approximately 14 billion years ago, so all matter in the visible Universe is within 14 billion light years of the Earth. However, the space the Universe occupies is only really finite if it's positively curved. If it's flat or negatively curved, the space it occupies is infinite, and if its density is constant, it must contain an infinite amount of matter even though we only see part of it. The Big Bang is a singularity - a point with infinite density. It's hard to get your head around intuitively, but it all makes sense mathematically. (The maths is pretty hard, and rarely covered at undergraduate level.) The simplest model in rough agreement with observations is called the Einstein-de Sitter Model, and it's flat with a zero cosmological constant. See http://www.britannica.com/science/cosmology-astronomy/Relativistic-cosmologies#ref1069808 http://www.britannica.com/science/cosmology-astronomy/Relati... More general models are covered here: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Solutions https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...

dsfuoi 10y ago
Radius of the visible universe is actually 45.7 billion ly.
- DonaldFisk 10y ago
  Thanks for the correction: https://en.wikipedia.org/wiki/Observable_universe https://en.wikipedia.org/wiki/Observable_universe

DougWebb 10y ago

Off the cuff thought: the overall universe is infinite and not expanding, and it's only the visible universe that's expanding into that infinite space. Now try to wrap your mind around this: someone that's one light year to the left is going to see a slightly different visible universe, also expanding, into the same infinite space. But if we look in their direction, we see the edge of our visible universe expanding into the void, but from their point of view looking in the same direction our edge is one light year short of their edge. So what's our edge expanding into?

Razengan 10y ago
I've always wondered; is there a "last" galaxy in any direction, such that for an observer in that galaxy, no further light or radiation can be detected from that direction? (outside that galaxy) That, must be a terrifying place to live in......
- hellameta 10y ago
  I don't see how our situation is any less terrifying haha
  - Razengan 10y ago
    It's certainly less terrifying than having to look at an infinite abyss.
    - hellameta 10y ago
      I really enjoy your belief that you're somehow not always looking at an infinite abyss :P
- Razengan 10y ago
  Too late to edit, but I must add that I'm not necessarily asking if there's an "edge" of the Universe.
  - deleted 10y ago

Retric 10y ago

Math includes the idea of orders of infinity. There are infinite prime numbers, there are more positive integers, even more integers (positive and negative), even more rational numbers (A/B), and even more numbers (rational + irrational {e, Pi} etc)...

pcmonk 10y ago
In what sense are there more rational numbers than prime numbers? They can be put into bijection with each other, so we generally think of them as being same infinity. There are more real nubmers, of course, by Cantor's diagonalization, so your basic point is true.
- Retric 10y ago
  The set of all prime numbers is contained within the set of rational numbers, but they are rational numbers that are not within the set of prime numbers. Cantor's diagonalization is simply demonstrating that same inequality by showing a number in set A is not in set B. Just because you can map two infinity's to each other does not mean they are of the same size consider: Limit(0->inifinity) of (x - (x/2)) algebraically that's clearly Limit(0->inifinity) of X/2 which is infinity. PS: What makes Cantor's diagonalization interesting is you can repeat it recursively an infinite number of times. This is more obvious in base 2.
  - JBiserkov 10y ago
    >Cantor's diagonalization is simply demonstrating that same inequality by showing a number in set A is not in set B. If that were true, why go to all the trouble, just show 1/2 which is not a natural number, or sqrt(2) which is not a rational number. Cantor's diagonalization is proving that no mapping exists between the natural numbers and the real numbers in [0, 1]; that no matter what mapping you (try to) come up, there will be a number you would miss. The primes and rationals have the same size (cardinality) as the natural numbers, namely countably infinite. See https://en.wikipedia.org/wiki/Countable_set#Formal_overview_without_details https://en.wikipedia.org/wiki/Countable_set#Formal_overview_...

gnodar 10y ago

I don't know the answer to your question, but I can imagine how something can expand if it's infinite. Imagine an infinitelylong rubber band in front of you. Now imagine grabbing it with two hands and pulling them away from each other, causing the rubber band to stretch. If you take a sharpie, and paint dots on a spot representing planets or whatever else, they will pull away from eachother as you stretch the rubber band.