1. Re: Universe size questions

Let us please keep this thread on topic and not stray off into the mist.

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3. Re: Universe size questions

hey nFA,
I am still trying to understand.

"But it shouldn't be factored out completely. The 3.5 factor represents, in Comoving Coordinates, the difference in length from where the CMB was when it was emitted and where it is now. Those are two different points. What happens is that one has this comoving coordinate for the CMB emission then and when one plugs that into the metric you get the 13 Bly distance. Then you get another distance now to the same comoving coordinate which is 46 Bly. So it's a little tricky. The comoving coordinate is the same but the distance to that coordinate has changed over the last 13 B yr."

ok, I understand that its the same Comoving Coordinate.
it has 2 different values.
one is the now value.
the other is the then value.
the now value is 46 Bly.
the then value is 13 Bly.
but its the same Comoving Coordinate.
I can understand that.

but what I do not understand is how this jibes with
the change in distance from 13 Bly to 46 Bly.
how did that distance increase?
by expansion of the universe, I would assume?
but I must be wrong.
I just don't know why I'm wrong.
and I think.
and I am not understanding.
can you possibly please shed any light on
this for me? (har har)

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6. Re: Universe size questions

Let us please keep this thread on topic and not stray off into the mist.
I think that we have kept it on topic.

I cited the fact that some ancient values based texts (philosophic and religious) have embraced this vast multiple world (preferably limited to observables IMO) idea in response to the question of how many folks think of this. I did not cite the sources or further indicate their content or affiliation.

I've repeatedly stressed that confusing texts in the values domain with scientific texts on the factual domain is a logical error, a category mistake.

Now, I think that many fans of the multiverse idea in the string theory community have allowed themselves to be influenced by these sources as inspiration and so they use the multiverse dodge as a lazy way to declare that physics is complete. "The random choice of fundamental constants in this multiverse is what makes them take their present values". I think that these string theorists are "off topic" by virtue of commiting this category error.

I'm with Feynman: philosophic or mystical preconceptions have no place in science. All science does is construct the most elegant model of the data.

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8. Re: Universe size questions

Originally Posted by chas53
hey nFA,
I am still trying to understand.

"But it shouldn't be factored out completely. The 3.5 factor represents, in Comoving Coordinates, the difference in length from where the CMB was when it was emitted and where it is now. Those are two different points. What happens is that one has this comoving coordinate for the CMB emission then and when one plugs that into the metric you get the 13 Bly distance. Then you get another distance now to the same comoving coordinate which is 46 Bly. So it's a little tricky. The comoving coordinate is the same but the distance to that coordinate has changed over the last 13 B yr."

ok, I understand that its the same Comoving Coordinate.
it has 2 different values.
one is the now value.
the other is the then value.
the now value is 46 Bly.
the then value is 13 Bly.
but its the same Comoving Coordinate.
I can understand that.
No, this isn't quite right. The old distance to the Comoving Coordinate of the CMB emission surface is 13 Bly. The current distance to the same Comoving Coordinate is 46 Bly. The same Comoving Coordinate had different distances at different times. You are mistaking the coordinate with the distance and they are separate concepts.

but what I do not understand is how this jibes with
the change in distance from 13 Bly to 46 Bly.
how did that distance increase?
by expansion of the universe, I would assume?
Yes, exactly so.

but I must be wrong.
I just don't know why I'm wrong.
and I think.
and I am not understanding.
can you possibly please shed any light on
this for me? (har har)
You are conflating two concepts, coordinate and distance, that are distinct.

Take a spherical surface, draw latitude and longitude coordinates on it. Inflate the sphere by a factor of 3.5 in comoving coordinates. The coordinates in the comoving coordinates (lat and long on the sphere) are unchanged. But the distance measured between them is now 3.5 times as great.

I think that should do it. The real problem, once this is overcome, is how the scale factor for the metric gives a factor of 1000. Let's leave that for another day after we cross this hurdle.

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10. Re: Universe size questions

Originally Posted by Gmetric
It's a good article. It avoids the distinction between comoving coordinates and proper distances skillfully though.

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12. Re: Universe size questions

yes thank you for posting that article Gmetric.
nFA, thank you again.
you are an excellent teacher.
thank you for your patience with me.
I understand now.
and I will be ready tomorrow or whenever you have time,
to move on to the next part, the scale factor for the metric gives a factor of 1000 problem.

good night nFA,
Charlie

13. Re: Universe size questions

Now for the factor of 1000 in CMB.....

I'm going to be looking for a place to live today so not much time.

There are two pieces that need to be looked at. One is the FLRW metric:

https://en.m.wikipedia.org/wiki/Frie...“Walker_metric

The metric is fundamental for calculating distances. You'll notice that it contains the scale factor a(t). But further in the article there are three different choices of comoving coordinates: reduced circumference, hyperspherical, and Cartesian. These are all comoving coordinates with different underlying geometry. As the latter part of the article shows this a(t) contains all the information about the expansion of the universe. There is a separate article about the scale factor.

https://en.wikipedia.org/wiki/Scale_factor_(cosmology)

In this article note that how a(t) depends upon t depends on which form of matter-energy dominates the pressure-density relationship (equation of state) at what time. By pressure - density relationship I mean "how does the pressure of the stuff depend on its density". This is different for the radiation dominated, matter dominated and dark energy dominated epochs.

The relationship between redshift and the a(t) ( 1 + z = a(now) / a(then) ) is derived from the FLRW metric here:
https://en.wikipedia.org/wiki/Redshi...cal_derivation

The CMB formed when electrons combined with protons to form hydrogen atoms which happened when the universe cooled to 3000K. The current temperature is about 3K. There is a direct relationship between the temperature of radiation in the universe and the scale factor a(t) provided by the redshift relation 1+z=a(now)/a(then).

So this says that the universe expanded by about 1000 fold in the scale factor since the CMB was formed.

But it is not directly interpretable as a distance just as differences in coordinates are not directly interpretable as distances.

To calculate distances, assuming that they are along a radial line so we can neglect differences in the angular coordinates, one needs to specify t and r and integrate the metric. So one has at the time of emission a time and radius. We observe them at r=0 (here) now, t = 13 Byr. When we integrate the metric to r of that point of emission now we get 46 Bly.

The 1000 scale factor and the 3.5 distance growth factor are only seemingly inconsistent. One uses the scale factor to calculate the distance growth factor. Algebra alone won't do it. One needs to do calculus and integrate the metric.

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15. Re: Universe size questions

hey nFA,
thank you.
I hope you find an excellent place to live.
I wanted to let you know that I see your post.

16. Re: Universe size questions

hey nFA,

here is another link to the FLRW metric, in case that one doesn't work:

https://en.wikipedia.org/wiki/Friedm...3Walker_metric

I have more reading to do at wikipedia.
and I will continue to try to understand this better.
thank you again for all of your excellent teaching.
Charlie

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