On 1/24/2020 6:58 PM, Alan Grayson wrote:
On Friday, January 24, 2020 at 3:50:54 PM UTC-7, Brent wrote:
On 1/24/2020 2:08 PM, John Clark wrote:
On Fri, Jan 24, 2020 at 3:06 PM 'Brent Meeker' via Everything
List <[email protected] <javascript:>> wrote:
//
>> If you're assuming that Real Numbers exist and that even a 1 cm
universe
would need a infinite number of labels
/> But not an infinite range of labels./
OK now it's official, I have no idea what you're talking about.
>> I ask my question again:
*What is the difference between a "finite" universe that
is expanding and accelerating and an infinite universe
that is expanding and accelerating?*
/> Imagine the Earth is expanding like a balloon and at an
accelerating pace. /
A balloon is a terrible analogy for the Earth and a inflating
balloon is an even worse analogy for a universe that will expand
and accelerate forever. With the balloon you're standing outside
of it watching the balloon expand into something that's already
there,
But you don't have to stand outside of it. Everything in the
analogy is observable for a Flatland creature living on the sphere.
but you can't stand outside of the universe and the universe is
not expanding into anything that's already there.
/> You can't go fast enough to circumnavigate it because
there's a speed limit. /
And to call that speed limit the speed of light would be true but
tends to trivialize it, really it's something far more
fundamental and profound, it's the very speed of causality.
So what. I'm making an analogy, not a model.
/> In your imagination is it finite or infinite? Are there
locations on it which are finite distances apart?Is there a
set of such locations connecting any two points? Is the sum
of the distances between locations of such a set finite?/
I would say a infinite amount of information would be needed to
adequately
Nobody asked about the amount of information. That's a red
herring that LC threw in. The question was about the expansion
and size of the universe.
describe the evolution of the phase space (all possible values of
the position and momentum of the particles in the universe) of
such a expanding accelerating universe. It's infinite because no
amount of approximation would be good enough for prediction, due
to the accelerated creation of new space there will always be
more values of position and momentum that particles can be in
tomorrow than they can be in today. By the way, all this talk
about the distance between particles in a expanding accelerating
universe is rather ambiguous if you don't specify when, and "now"
has no meaning everybody agrees with.
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
As in my analogy, in a finite universe there are a finite number
of intervals of finite distance that can link any two points in
the universe. Of course this refers to it being finite at a given
time, and you raised the problem of defining what counts as "at
the same time". The answer is that it is at the same time if it
is at the same degree of expansion...operationally it means that
two distant events are "at the same time" if the isotropic
temperature of the CMB looks the same to them.
Brent
*You sometimes refer to the scale factor in GR being a function of
time, namely a(t). But in relativity each observer has a clock, and
time is what the observer reads on his clock. So what time are you
referring to; the clock of a bird's eye observer outside the universe?
TIA, AG
*
In the equation "t" is just a parameter. The physical clock is the
expansion itself, which is most conveniently measured by the CMB
temperature. But if you read Ned Wright's tutorial he points out that
there are different ways to assign a size to the observable universe
because of the frame dependence of simultaneity.
Brent
and accelerating forever and an infinite universe that is
expanding and accelerating forever?
John K Clark
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