On Sunday, January 26, 2020 at 1:20:53 AM UTC-6, Philip Thrift wrote:
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>
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> On Saturday, January 25, 2020 at 10:47:55 PM UTC-6, Brent wrote:
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>>
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>> On 1/25/2020 6:10 PM, Lawrence Crowell wrote:
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>> On Saturday, January 25, 2020 at 6:49:36 PM UTC-6, Brent wrote:
>>>
>>>
>>>
>>> On 1/25/2020 4:32 PM, Lawrence Crowell wrote:
>>>
>>>
>>>
>>> On Saturday, January 25, 2020 at 6:23:54 AM UTC-6, John Clark wrote:
>>>>
>>>> On Fri, Jan 24, 2020 at 5:21 PM Bruce Kellett <[email protected]>
>>>> wrote:
>>>>
>>>> >> And I've heard a bunch of bad analogies but I still haven't heard a
>>>>>> direct answer to my question:
>>>>>> What is the difference between a "finite" universe that is expanding
>>>>>> and accelerating forever and an infinite universe that is expanding and
>>>>>> accelerating forever?
>>>>>>
>>>>>
>>>>
>>>> *> If you don't understand Brent's answer in terms of the range of
>>>>> values in coordinate maps, then you will never understand the difference.*
>>>>>
>>>>
>>>> Then I guess I'll never understand the difference.
>>>>
>>>>
>>>>> > A finite universe has a finite range of coordinate values.
>>>>>
>>>>
>>>> NOPE! Brent specifically said "*I'm assuming a continuum spacetime. So
>>>> even a 1cm interval takes an infinite number of labels*". Thus even
>>>> if the universe is not expanding at all and even if it's only 1cm across a
>>>> infinite number of labels with a infinite rage of coordinate values
>>>> printed on them would be needed.
>>>>
>>>
>>> Nope. Space and spacetime are an epiphenomenology. They are mental
>>> perceptual models that result from large N-entanglements of quantum states.
>>> There are no infinite sets of points and labels, that would in fact be
>>> uncountably infinite. These things only exist in our mathematical
>>> representations or axiomatic systems. Now, what information we can get
>>> about space from the IR domain of energy at extreme distances, such as with
>>> burstars etc,, is the representation of what we call space being smooth
>>> fits the data. This does not mean that fundamentally there is an actual
>>> smooth continuum of space.
>>>
>>>
>>> I don't disagree, but you're getting further and further from saying
>>> what it means for spacetime to be finite versus infinite. Since it's our
>>> mathematical model, that should have a simple mathematical answer.
>>>
>>> Brent
>>>
>>
>> There seems to be some sort of issue with the idea of continuum or space
>> having an infinite number of points. I see this as a modern day version of
>> asking how many angels can dance on a pin.
>>
>>
>> I have no issue with it. But it doesn't mean that a spherical spacetime
>> is infinite. The infinity of metric distance in a Riemannian space is not
>> the same as the infinite cardinality of point in a real interval.
>>
>> Brent
>>
>
>
>
> If the Universe is truly infinite, if you travel outwards from Earth,
> eventually you will reach a place where there's a duplicate cubic meter of
> space. The further you go, the more duplicates you'll find.
>
> Ooh, big deal, you think. One hydrogen pile looks the same as the next to
> me. Except, you hydromattecist, you'll pass through places where the
> configuration of particles will begin to appear familiar, and if you
> proceed long enough you'll find larger and larger identical regions of
> space, and eventually you'll find an identical you. And finding a copy of
> yourself is just the start of the bananas crazy things you can do in an
> infinite Universe.
>
> In fact, hopefully you'll absorb the powers of an immortal version of you,
> because if you keep going you'll find an infinite number of yous. You'll
> eventually find entire duplicate observable universes with more yous also
> collecting other yous. And at least one of them is going to have a beard.
>
> So, what's out there? Possibly an infinite number of duplicate observable
> universes. We don't even need multiverses to find them. These are duplicate
> universes inside of our own infinite universe. That's what you can get when
> you can travel in one direction and never, ever stop.
>
> Whether the Universe is finite or infinite is an important question, and
> either outcome is mindblenderingly fun. So far, astronomers have no idea
> what the answer is, but they're working towards it and maybe someday
> they'll be able to tell us.
>
> https://phys.org/news/2015-03-universe-finite-infinite.html
>
> @philipthrift
>
This is the case for a spatial surface that is infinite, but distance is
using the idea of Poincare recurrence around 10^{10^{100}} light years
away. This is far beyond the cosmological horizon and you could never get
there no matter how long or extremely you try to accelerate outwards. With
the spherical universe much the same also holds, but where getting around a
spatial sphere with an enormous radius of curvature is impossible because
it will always expand faster than you can travel. With the flat spacetime
the existence of repeated versions of this local world means there is some
covering space that is a torus or maybe the Poincare dodecahedral space. I
tend to think this covering space is some form of quasi-crystal. For all we
know we are in a cosmos with that sort of space.
LC
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>
>
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