What is the accepted diameter of the universe?

[Voltage]

It seemed to me earlier that you were arguing for an upperbound on the size (it can't be any larger than such and so) by starting with an idea of the size at the start of expansion and by assuming some kind of bound on the SPEED of expansion.

I suppose I was. But I didn't mean to argue, I just wanted to find out what the currently accepted figure was for the size of the universe and be able to give a "reasonable" explanation. Maybe I was being too assumptive.

Mainstream cosmology, whatever's based on classic einstein GR, does not HAVE any limit on expansion speed. It can be any finite speed and to talk about the size (of the whole thing) at the start of expansion you have to go outside the bounds of classic 1915 einstein.

I'm a big fan of Einstein. I've read up on the original GR translation plus other material. I like to think I stick closer to Einstein than other people do. But they don't always agree that I do.

as far as we know, singularities do not exist in nature, they only exist where theories break down, so its not meaningful to talk about the starting size in classic GR.

Agreed wholeheartedly. But have you ever heard of the Weinberg interpretation? I'd say it's not necessarily the whole theory that breaks down, but some aspect of it, or some interpretation. String Theory has morphed to a huge degree, why can't GR move a little and still stay as GR?

they only do that in popularization books, where they talk about the tiny size of what eventually became the observable universe, they never talk about the initial size of the whole thing because the size of a singularity is not well-defined. that's all pop sci anyway.

IMHO there are no infinities and no singularities in nature. My goal is to make science more popular. I mean that marcus.

there are quantized models where you don't have a singularity and then you can talk about the size at the moment of BOUNCE which replaces the singularity, so you can talk about the initial size at the start of expansion but to do it you have to go outside the bounds of the classic 1915 theory, and its hard.

I definitely don't buy bounce. That's no explanation at all. Going beyond the bounds of "classic 1915 theory" is what Einstein was trying to do, and I try to stick with Einstein, so I suppose that's where I'm going.

So I don't think you or anyone can get a grip on the size of the universe that way----mainly because there is no known bound on the speed of expansion.

See your earlier point, I guess I was arguing that the ½c² for 13.7 billion years gave an upper bound.

I think the only way to get a handle on it is by measuring Omega, essentially measuring the large scale curvature. But if you want, boil your argument down to a brief message that says roughly how it goes and send it PM and I will look at it. I may not be able to comment helpfully, but I'm curious, so you are welcome to do it if you want.

I need to give it some thought.

 

[marcus]

But I didn't mean to argue, I just wanted to find out what the currently accepted figure was for the size of the universe and be able to give a "reasonable" explanation.

I didn't mean arguing in a bad sense. I meant that you were giving a logical argument---a rational deduction---about the size, based on some assumptions.

that's good. we are supposed to be doing that.

But I question your assumptions. I think your chain of reasoning breaks down because if you base things on Einstein GR then you can't say how big it was when it started expanding

AND (this is more important) you can't put a limit on the speed of expansion.

Einstein does not let you put a limit on the speed with which distances increase.

I can't respond to all of your separate points, but I'm glad you are thinking about it. Towards the end of your post where you quote me

I think the only way to get a handle on it is by measuring Omega, essentially measuring the large scale curvature...

You say

I need to give it some thought.

I hope you do give more thought to using curvature to estimate size. It is the only way I've ever known any cosmologist to do it. For example that is how Cornish et al get their basic underlying distance scale--they use the radius of curvature as their benchmark.

Again, the reason you can't use a bound on expansion speed to estimate size is because Einstein does not let you.

(His 1905 theory now called "special" relativity has a speed limit on certain kinds of motion but that does not apply to expansion of distances and it only can be applied in certain limited, i.e. special, cases. Two things within the same flat or nearly flat reference frame----not widely separated. His later theory, which he called "general", trumps the earlier 1905 theory

 

[Voltage]

I think your chain of reasoning breaks down because if you base things on Einstein GR then you can't say how big it was when it started expanding.

I was thinking of something very small compared to the current size marcus, so small that I can "reasonably" consider it to be zero.

AND (this is more important) you can't put a limit on the speed of expansion. Einstein does not let you put a limit on the speed with which distances increase.

I thought there was a limit that I could apply as at now. A while back you said that distances expand 1% every 140 million years. Working back from that they've expanded circa 7% in the last billion years, and 100% in the 13.7billion year age of the universe. This is why I thought ½c² seemed "reasonable" as the radius the universe. Perhaps I should have said d=x² where d is the diameter in billions of light years and x is the age of the universe in billions of years. This means the universe is 13.7 x 13.7 = 187 billion light years across now. A billion years ago it was 12.7 x 12.7 = 161 billion light years across, so it's expanded by 26 billion light years in the last billion years. Two billion years ago it was 11.7 x 11.7 = 137 billion light years across, so it expanded 24 billion light years in that billion year period.

The mental picture I've got is that of a universe that's akin to the "ball of gas" you mentioned earlier. It's more like a sphere of light that moves outwards in all directions at the speed of light, and also swells because there's no bag to hold it back. This is the only energy that exists. Whilst some of it is tied up as matter, there is no "outside" to the sphere, because beyond it, no energy means no gravity means no space. It's flat, it's open, it's a runaway, but it isn't a 4-sphere, there's no radius of curvature to bring you back on yourself, and it isn't infinite.

But sheesh, reading up on that conformal gravity reminded me just what a total layman amateur I am. I'd be grateful if you could put me straight on all this. Thanks for all the time you've put in so far. Meanwhile I'll read up on that radius of curvature.

 

[marcus]

I was thinking of something very small compared to the current size marcus, so small that I can "reasonably" consider it to be zero.

that is fair enough. I apologize for quibbling.

But that percentage rate only applies to the present. In the past the percentage increase per unit of time was much larger.

Maybe I should have said that distances are currently expanding at a rate of 1/10% every 14 million years.

I thought there was a limit that I could apply as at now. A while back you said that distances expand 1% every 140 million years. Working back from that they've expanded circa 7% in the last billion years, and 100% in the 13.7billion year age of the universe. This is why I thought ½c² seemed "reasonable" as the radius the universe.

Alas, I have misled you! I have not made things clear enough and you have gotten a mistaken idea. sincere apologies

You must have heard of people seeing quasars at redshift z = 7.
that means that the universe has expanded EIGHT-FOLD since the light left them on its way to us. You always add one to the redshift to get the ratio by which the universe has expanded.

You probably have heard that the redshift of the CMB is about 1100. that means that the universe has expanded about 1100-fold during the time that light has been traveling towards us from whatever emitted it (when the universe was an estimated 380,000 years old). To be pedantic one could say by a factor of 1101, but the figure 1100 is only accurate to two decimals.

I want to try to help you understand and I see you trying to estimate z-factors for various times in the past. There is an online CALCULATOR for that. this will give you an accurate figure for how much the universe has expanded in the last 1 billion years, or in the last 2 billion years

http://www.astro.ucla.edu/~wright/DlttCalc.html

Your rough-and-ready calculation is a good try but the expansion history is a little more complicated and these online cosmology calculators really come in handy.

Put in 1.0 over on the left where it says "light travel time in Gyr" and press "general" (dont change the default settings)
You should get z = 0.077 over at the right. That means the universe has expanded by a ratio of 1.077 in the past billion years.
or grown by 7.7 percent. about what you estimated!

Now put in 2.0 billion years and you should get a 16.2% expansion----the ratio is 1.162.

Keep on going. You can compare it with your rough and ready estimates here:

Perhaps I should have said d=x² where d is the diameter in billions of light years and x is the age of the universe in billions of years. This means the universe is 13.7 x 13.7 = 187 billion light years across now. A billion years ago it was 12.7 x 12.7 = 161 billion light years across, so it's expanded by 26 billion light years in the last billion years. Two billion years ago it was 11.7 x 11.7 = 137 billion light years across, so it expanded 24 billion light years in that billion year period.

If you put in 10.0 billion years you should get that the expansion during that time has been by a factor of 2.815

In the past 13.0 billion years the expansion has been by a factor of 8.872

The calculator is set to arbitrarily cut off when it gets to BILLION-FOLD expansion. AFAIK You cannot make it give you a z bigger than a billion minus one.
It is really not meant to take up that close to the beginning of expansion.

=====================
ACCORDING TO MY MENTAL PICTURE best on Wright's 'best fit', at the present moment the radius of curvature is 130 billion LY. So if I use Wright's calculator and go back 13.666 billion years, that means the radius of curvature was 130 light years.

If I trust the accuracy of his calculator back to such early days, then that would be my best estimate of the size of the universe at 13.666 billion years before present.

Apart from looking at curvature, that is looking at astronomers measure of Omega, I don't think there is any other way to get a grip on the size.

But sheesh, reading up on that conformal gravity reminded me just what a total layman amateur I am. I'd be grateful if you could put me straight on all this. Thanks for all the time you've put in so far. Meanwhile I'll read up on that radius of curvature.

You are very gracious! I enjoy talking about this stuff. We all just do the best we can and I'm no great expert either. I can tell you are still picturing a surrounding space for the universe to expand into.
that isn't part of orthodox cosmology---but we can get to that another time
have fun

 

[Voltage]

Thanks for all this marcus. I'll have fun with that calculator.

..I can tell you are still picturing a surrounding space for the universe to expand into. That isn't part of orthodox cosmology...

Not at all. My picture is a whole lot less orthodox than that!

:)