How can we calculate universe diameter at a given time

[Quarlep]

How can we calculate universe dimater at a given time ?

 

[phinds]

How can we calculate universe dimater at a given time ?

The universe is not known to HAVE a diameter so it would be tough to calculate.

The observable universe has a diameter, currently about 90+ billion light years, centered on your left eyeball (when you have your right eye closed).

 

[Quarlep]

http://cosmology.berkeley.edu/~yuki/cosmos/ look this "How does the universe evolved ?" How the physicists calculate that horizon sizes

 

[phinds]

You need to be more specific. I'm not going to read that entire website to try to figure out what your question is.

 

[Quarlep]

I have already gave the spesific part. In bottom there's a table and there's horizon size How they calculate it ?

 

[phinds]

I have already gave the spesific part. In bottom there's a table and there's horizon size How they calculate it ?

No, you had not given a specific at all, but now you have, although your statement "In bottom there's a table" was very misleading since the table is in the middle of the long page, not at the bottom.

It is a reasonable question, but I don't know specifically how how they calculated those horizons. I can tell you in general that many of the calculations after what they call decoupling were based on estimates of the age of the universe derived from red-shift and other information and extrapolated back from the known age of the universe.

 

[Bandersnatch]

Head to this site:
http://cosmocalc.wikidot.com/advanced-user
It shows the equations used by the LightCone calculator made by one of the forum members (Jorrie): http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
You'll find ##D_{hor}## and ##T## for the horizon distance and cosmic time. These are all functions of redshift and Hubble parameter.

 

[Chalnoth]

I have already gave the spesific part. In bottom there's a table and there's horizon size How they calculate it ?

The horizon size is a function of the combination of the speed of light with the expansion history.

If we wait forever, a photon that leaves the Earth today will only barely reach the matter that is currently at our cosmological horizon. We can never communicate with any matter that is currently further than this.

 

[Stan Stuchinski]

http://cosmology.berkeley.edu/~yuki/cosmos/ look this "How does the universe evolved ?" How the physicists calculate that horizon sizes

Thanks for the link, Quarlep; I have been searching various sources for WEEKS for a tabular chart showing this information. Although there ARE a few gaps and I am confused by some of the data, it is a big help and I appreciate your sharing.

Stan

 

[Chronos]

That only accounts for the size of the observable universe. It does not take into account the possibility the universe may have always been spatially infinite, nor that it may be much larger than its particle horizon.

 

[marcus]

How can we calculate universe dimater at a given time ?

Quarlep, do you know what the Hubble radius is? Would you be satisfied to know how to calculate that distance, at any given time.
It is sometimes referred to a a cosmic "horizon", so maybe you have been reading about the Hubble radius and thinking of it as a measure of size of universe. I think in that "Yuki" UCBerkeley material you linked to, the Hubble radius was at one point called the horizon.

The Hubble radius increases over time and gradually converges to a distance beyond which signals we might send cannot reach and from beyond which galaxies' light cannot reach us.

The Hubble radius at anyone given time is the size of distances which are increasing at speed of light. So if a galaxy is today at that distance and sends us a flash of light, that flash would at least for the time being not make any progress. Because the distance it would have to travel would be growing at the same speed as the light was advancing.

At present that R is 14.4 billion light years. It has been growing throughout history and will continue as far as we know.

It can be calculated for any given year of universe time--is that what you are asking about?

I don't think anyone knows the actual diameter of the universe, it might not have a diameter because it is infinite. That is now well-defined and nobody bothers with it. When they use words like radius and diameter they are usually talking about stuff like the Hubble radius, i.e. horizon type stuff.

 

[Stan Stuchinski]

That only accounts for the size of the observable universe. It does not take into account the possibility the universe may have always been spatially infinite, nor that it may be much larger than its particle horizon.

Quarlep, do you know what the Hubble radius is? Would you be satisfied to know how to calculate that distance, at any given time.
It is sometimes referred to a a cosmic "horizon", so maybe you have been reading about the Hubble radius and thinking of it as a measure of size of universe. I think in that "Yuki" UCBerkeley material you linked to, the Hubble radius was at one point called the horizon.

The Hubble radius increases over time and gradually converges to a distance beyond which signals we might send cannot reach and from beyond which galaxies' light cannot reach us.

The Hubble radius at anyone given time is the size of distances which are increasing at speed of light. So if a galaxy is today at that distance and sends us a flash of light, that flash would at least for the time being not make any progress. Because the distance it would have to travel would be growing at the same speed as the light was advancing.

At present that R is 14.4 billion light years. It has been growing throughout history and will continue as far as we know.

It can be calculated for any given year of universe time--is that what you are asking about?

I don't think anyone knows the actual diameter of the universe, it might not have a diameter because it is infinite. That is now well-defined and nobody bothers with it. When they use words like radius and diameter they are usually talking about stuff like the Hubble radius, i.e. horizon type stuff.

Thanks for adding to the conversation, my friends; I found your comments very helpful.
I have a few questions, but I think as a preface, I need to define my views regarding a few concepts concerning the diameter of the universe:
Subjective View # 1: I don’t accept ANYTHING as being “infinite.” Maybe I’m just being anal retentive (I’ve been called that more than once!), but I find the concept of an infinite universe as being unacceptable; I like “order” in my world, and an infinite cosmos (to ME, anyway) flies in the face of a clearly defined universe.
Subjective View # 2: I understand that there is a difference between the “observable” universe and the (as yet) “UN-observable” (beyond our light cone) universe.
Subjective View # 3: I do not accept the parallel universes concept (Everett’s many world’s interpretation of quantum physics), the term meaning that there are an infinite number of side-by-side universes with carbon copies of me in them, differing only in minor details (i.e. occupation, hair color, etc, ad infinitum). To me, hat’s just too “messy,” with a vast overabundance of realities!
Subjective View # 4: HOWEVER, I am a big believer in the Multiverse, each universe differing in physical properties and constants, mainly because this neatly solves the anthropic problem of why our universe is so “finely tuned for intelligent life.”
Now, on to my questions:
Question # 1: On Yuki’s excellent “How has the universe evolved” chart, his column # 5 is labelled “Horizon Size.” I am assuming that this is the diameter of the OBSERVABLE universe. Am I correct in this assumption?
Question # 2: In the “Horizon Size” column, diameters are given in meters and light years… with one exception: Row 5 (End of Inflation), he gives the diameter simply as “1” with no units. “1” what?
Question # 3: Assuming Yuki’s chart gives the diameter of the OBSERVABLE universe. Is there a chart, graph, or simple formula that gives the diameter of the UNobservable universe, as well? The reason I ask this question is that I usually think of the diameter of the universe after inflation in the commonly referred to terms as “being 10 centimeters in diameter, about the size of a grapefruit.” However, I recently viewed a YouTube video by a practicing astrophysicist as giving the diameter of the universe after inflation as being .16 light years in diameter; B-I-G difference. So I am assuming this latter figure is for the UNobservable universe; am I correct in my assumption?
Question # 4: Regarding the Multiverse… We have the OBSERVABLE universe, and the UN-OBSERVABLE universe (which is always larger). So where would the bubbles of the multiple Multiverses reside? Would they occupy space outside of the UN-observable universe?
Thanks in advance, Chronos and Marcus, for your time and consideration,
Stan

 

[Quarlep]

It can be calculated for any given year of universe time--is that what you are asking about?

I was asking in early universe when Inflation happened I see somewhere that we can calculate it to think a light cone as somebody say above.Inflation theory happened that time 10^-35 but at that time universe diameter is 10^-35xc =10^-27m. In early universe I guess we can calculte universe diameter but know we can't cause we can see only part of the universe.

 

[Quarlep]

hanks for the link, Quarlep; I have been searching various sources for WEEKS for a tabular chart showing this information. Although there ARE a few gaps and I am confused by some of the data, it is a big help and I appreciate your sharing.

I am very happy If helped you

 

[Chronos]

Subjective View # 1: I don’t accept ANYTHING as being “infinite.” Maybe I’m just being anal retentive (I’ve been called that more than once!), but I find the concept of an infinite universe as being unacceptable; I like “order” in my world, and an infinite cosmos (to ME, anyway) flies in the face of a clearly defined universe.

Many scientists share your revulsion at the notion of an infinite [or infinitesimal] anything. It usually leads to paradoxes - e.g., Olber's Paradox. The universe, however, is a special case and we have no observation that prohibits it from being infinite. A finite universe is, in fact, an oxymoron that provokes illucid questions like - what lays outside the universe?

Subjective View # 3: I do not accept the parallel universes concept (Everett’s many world’s interpretation of quantum physics), the term meaning that there are an infinite number of side-by-side universes with carbon copies of me in them, differing only in minor details (i.e. occupation, hair color, etc, ad infinitum). To me, hat’s just too “messy,” with a vast overabundance of realities!

Your objection is logical. An infinitude of parallel universes is, IMO, unaesthetic and almost surely paradoxical.

Question # 1: On Yuki’s excellent “How has the universe evolved” chart, his column # 5 is labelled “Horizon Size.” I am assuming that this is the diameter of the OBSERVABLE universe. Am I correct in this assumption?

Yes, column 5 is the causal, or particle horizon of the universe.

Question # 2: In the “Horizon Size” column, diameters are given in meters and light years… with one exception: Row 5 (End of Inflation), he gives the diameter simply as “1” with no units. “1” what?

Within the context of this presentation, I infer it to mean 1 meter.

Question # 3: Assuming Yuki’s chart gives the diameter of the OBSERVABLE universe. Is there a chart, graph, or simple formula that gives the diameter of the UNobservable universe, as well? The reason I ask this question is that I usually think of the diameter of the universe after inflation in the commonly referred to terms as “being 10 centimeters in diameter, about the size of a grapefruit.” However, I recently viewed a YouTube video by a practicing astrophysicist as giving the diameter of the universe after inflation as being .16 light years in diameter; B-I-G difference. So I am assuming this latter figure is for the UNobservable universe; am I correct in my assumption?

Yuki displays a chart of physical size vs horizon size of the universe further down the page, but, beware, it can be highly misleading. None of these figures have observational support, and subtly incorporate the assumption the universe originated as a singularity.The size of the universe following inflation depends heavily on assumptions. The inflation model was intended to resolve problems in a universe without inflation - like the horizon problem, flatness problem, etc. Inflation is an effective theory. For it to be viable, it must result in a universe that approximates the one we observe today. To achieve this goal, the universe must have expanded by an enormous amount in a very, very short interval of time. That number turns out to be about 60 e-folds [a factor of about 10^27 in lay terms]. Again, different models predict a different number of e-folds, but, it is generally agreed it cannot be much less that about 60 e-folds.

Question # 4: Regarding the Multiverse… We have the OBSERVABLE universe, and the UN-OBSERVABLE universe (which is always larger). So where would the bubbles of the multiple Multiverses reside? Would they occupy space outside of the UN-observable universe?

In string theory, the answer would be the 'bulk' - a hypothetical higher dimension wherein these 'bubbles' float around. Again, I caution we have no tangible evidence of any universe outside our own, so that should be taken with a solar mass grain of salt. To avoid confusion or bias, I elect to decline further comment.

 

[lightandmatter]

The universe is not known to HAVE a diameter so it would be tough to calculate.

The observable universe has a diameter, currently about 90+ billion light years, centered on your left eyeball (when you have your right eye closed).

Does that mean my left eyeball can see parts of the universe that my right eye can't see. What happens then when both eyes are open. [emoji3]

 

[phinds]

Does that mean my left eyeball can see parts of the universe that my right eye can't see. What happens then when both eyes are open. [emoji3]

When both eyes are open your observable universe is centered on the bridge of your nose. If you are cross-eyed, you have two observable universes.

 

[OCR]

If you are cross-eyed, you have two observable universes.

That seems is left right, according to my observables... lol

 

[Stan Stuchinski]

Many scientists share your revulsion at the notion of an infinite [or infinitesimal] anything. It usually leads to paradoxes - e.g., Olber's Paradox. The universe, however, is a special case and we have no observation that prohibits it from being infinite. A finite universe is, in fact, an oxymoron that provokes illucid questions like - what lays outside the universe?
Your objection is logical. An infinitude of parallel universes is, IMO, unaesthetic and almost surely paradoxical.
Yes, column 5 is the causal, or particle horizon of the universe.
Within the context of this presentation, I infer it to mean 1 meter.
Yuki displays a chart of physical size vs horizon size of the universe further down the page, but, beware, it can be highly misleading. None of these figures have observational support, and subtly incorporate the assumption the universe originated as a singularity.The size of the universe following inflation depends heavily on assumptions. The inflation model was intended to resolve problems in a universe without inflation - like the horizon problem, flatness problem, etc. Inflation is an effective theory. For it to be viable, it must result in a universe that approximates the one we observe today. To achieve this goal, the universe must have expanded by an enormous amount in a very, very short interval of time. That number turns out to be about 60 e-folds [a factor of about 10^27 in lay terms]. Again, different models predict a different number of e-folds, but, it is generally agreed it cannot be much less that about 60 e-folds.
In string theory, the answer would be the 'bulk' - a hypothetical higher dimension wherein these 'bubbles' float around. Again, I caution we have no tangible evidence of any universe outside our own, so that should be taken with a solar mass grain of salt. To avoid confusion or bias, I elect to decline further comment.

Thanks, Chronos, for your feedback on my thoughts and questions; it cleared up some of my muddled thinking.

Stan

 

[Quds Akbar]

We cannot, the universe is infinite in the sense that we cannot measure, the terms observable universe and universe go hand in hand with each other, we may be able to calculate the diameter of the observable universe, but it will always be larger, an alien on Andromeda galaxy for example is further away from us and therefore sees further out into space and the same thing applies to us, we can observe parts of the universe that he cannot. The universe is humongous, to say the least.

 

[marcus]

How can we calculate universe diameter at a given time ?

This is a good question. No one has (so far in this thread) given an answer in light years for the radius of the observable universe at this present time. That would be somewhere definite to start.
the interesting part of the question is "how can we calculate...?"

What is the distance NOW to the farthest matter that we can have so far received light from?

That is the same as asking how far a flash of light can have traveled since the start of expansion.

And I mean how far can it have traveled by now. If we measure time in "Qdays" of 17.3 billion years then now is 0.797 Qdays. Or about 0.8.

So the calculation will be an integral from 0 to 0.8 and each little step cdx that the light takes at time x has been enlarged by a stretch factor S(x) which tells how much distance has grown since time x up to now.

That stretch factor we know (from another thread) to be

$$S(x) = \frac{1.311}{\sinh^{2/3}(\frac{3}{2}x)}$$

the answer will be a distance in units of 17.3 billion light years. that is the natural unit if you measure time in Qdays.

 

[marcus]

What should the answer be, roughly? As I recall the distance NOW to the farthest matter we can so far have gotten light from is called the "particle horizon" in cosmology. And it is about 46 billion light years. So let's divide that by 17.3 billion light years and see what to expect.
46/17.3 = 2.66
The "particle horizon" is considered by cosmologists to be the radius of the observable universe.
Practically, we can't see quite that far because the very very early universe was dense hot plasma and it was not transparent, so light could not get thru.
But maybe something else, like if there were massless neutrinos, could get thru, so that in principle we could see that far.
So with the instruments we have we can see almost to the particle horizon, the CMB ancient light is from matter that is now about 45.5 billion light years. You can get a more exact figure just by opening Lightcone. It is the D_now corresponding to S = 1090, at the top of the table. that is the stetch of the CMB ancient light.

 

[marcus]

Anyway let me try doing the integral, to get the radius now of the currently observable. I'm using a Mac laptop and the math package is called "grapher" so I click on "grapher"
and type in 1.311 |sinh(1.5x)|^(-2/3)
press return, and select "Integration" from the "equation" menu
and type in the limits 0 and 0.8 (the lower and upper limits of integration).

Let's see what happens.

I was cautious and put in a small cut-off 0.00001. The integral came out 2.662 which was sort of what I expected. You can't push too close to the start of expansion because the stretch factor goes infinite. Curvature goes out of control. And what may count for more in this case is that the exponent 2/3 is no good when radiation becomes the dominant form of energy density. In a universe full of radiation you want exponent 1/2 because radiation behaves differently under compression and expansion.
So I integrated not between 0 and 0.8 but between 0.00001 and 0.8

Then I replaced the 1.5 by 2 and the 2/3 by 1/2 and covered the last little bit from zero to 0.00001, and I got 0.0059.
So in a quick and dirty patchwork way I got the answer 2.662+0.0059 = 2.668
That was integrating the whole way from 0 to 0.8
but for the first segment, where radiation is dominant, the better thing to integrate is
1.311 |sinh(2x)|^(-1/2)
So I integrated that up to 0.00001
and then went the rest of the way up to the present 0.8 with
1.311 |sinh(1.5x)|^(-2/3)
which is good when matter is the dominant part of the energy density.

 

[marcus]

How can we calculate universe diameter at a given time ?

So that is one way to answer. We calculated the radius of the observable---the socalled "particle horizon"---the distance now to the farthest matter we could in principle have gotten some signal from---I think of it as the distance a flash of light can have traveled since the start. If it didn't get blocked or scattered somewhere along the way.

To make the calculation easy we first divided the time by a Qday of 17.3 billion years, to get the time in Qdays.
And we integrated this between time 0 and time 0.8:
$$S(x) = \frac{1.311}{\sinh^{2/3}(\frac{3}{2}x)}$$
A small adjustment was made for the stretch between 0 and 0.00001, which did not add much, but basically that was it.
And we got the answer 2.668 which is the distance in "LightQday" units of 17.3 billion light years
So I need to multiply 2.668x17.3 to get the answer back into conventional earth-year terms.
It comes out 46.16 billion light years. that is the distance NOW over which the light has traveled and signifies the radius (so far) of the observable universe.

 

[Chronos]

The observable universe NOW for an observer in the Andromeda galaxy appears to be 2.5 million years older than our observable universe. But, you must keep in mind we will not observe the same photons currently observed by Andromeda aliens for another 2.5 million years due to the finite speed of light.

 

[Chalnoth]

The observable universe NOW for an observer in the Andromeda galaxy appears to be 2.5 million years older than our observable universe. But, you must keep in mind we will not observe the same photons currently observed by Andromeda aliens for another 2.5 million years due to the finite speed of light.

How did you arrive at this conclusion?

I'm pretty sure that an observer "now" would, by definition, observe the same age of the universe.

Unless by "now" you mean the aliens we could currently see observing from Andromeda, if we had the instruments to do so. Those aliens would observe a universe that is 2.5 million years younger.

 

[Chronos]

Yes, despite noble intent, I didn't entirely evade the simultaneity trap. If we had telescopes sufficient to view Andromedan astronomers at work, they would be viewing a universe 2.5 million years younger than ours. I agree the observable universe NOW is the same age for any observer anywhere in the universe. But, it is unique for each observer. Some events observed NOW lay in the future, and others in the past light cone of any other observer.

 

[Quarlep]

Thanks marcus.I understand cause of your explanation.That sinh^2/3(1.5x) Thats really helped me to understand universe evolution.

 

[nograviton]

How can we calculate universe dimater at a given time ?

People today notion that we live in the vast universe

The diameter of the universe is now 93 billion light years
Light year is the distance that light travels in one year
The speed of light is 300,000 km / second.
A day with 86,400 seconds
So one year 300,000 km light multiplied by 86,400 seconds multiplied by 365 days = 9.460.800.000.000 Kilometre
Nine thousand four hundred and sixty billion, eight hundred million kilometers
Wide universe 93 billion light years !

 

[Drakkith]

Wide universe 93 billion light years !

Indeed it is! And that's just the part we can see!

 

[nograviton]

Indeed it is! And that's just the part we can see!

Because World is non Realism. Phật pháp đã dạy !

 

[madness]

Why can't we estimate the size of the universe from the curvature of space? As far as I know, we have some empirical bounds on how flat the universe appears to be. From this, we could place bounds on how large it would be if it were a sphere, for example. Of course, we would need to make some assumptions, such as that the universe is globally similar to what we see locally.

I'm happy to be corrected by someone more knowledgeable here, but intuitively this seems to make sense to me.

 

[marcus]

Why can't we estimate the size of the universe from the curvature of space? As far as I know, we have some empirical bounds on how flat the universe appears to be. From this, we could place bounds on how large it would be if it were a sphere, for example. Of course, we would need to make some assumptions, such as that the universe is globally similar to what we see locally.

I'm happy to be corrected by someone more knowledgeable here, but intuitively this seems to make sense to me.

That's a clever observation. We can in fact estimate in the limited sense of giving a LOWER BOUND on the radius of curvature, or on the circumference.

As I recall this was done in one of the WMAP5 reports (the fifth year WMAP publications), as a kind of footnote. As you say it involves assumptions. You say "how large it would be if it were a sphere".
And "globally similar to what we see..."

Let's say we measure the spatial curvature and find a 95% confidence interval that Ω is between 0.99 and 1.01.
So we have an upper bound on the spatial curvature number |Ω_k| < 0.01

We take the current Hubble radius 14.4 Gly and we divide it by the square root of that number and that gives a 95% CONFIDENCE LOWER BOUND on the current radius of curvature of space.

144 Gly. The radius of curvature could be vastly bigger than that or it could be infinite. After all ZERO is in the confidence interval for the curvature number---zero curvature corresponds to infinite radius of curvature. but with 95% confidence the curvature is at most such and such so the radius is at least 144 billion light years.

The mental picture is of a 3D skin of a 4D ball except that the solid ball does not exist, is not actual. Only the 3D hypersphere exists. And it has a radius of curvature 144 Gly. So you can multiply by 2π and get its circumference. If you could pause expansion to make it possible to circumnavigate or send a flash of light around that circumference would indicate how long before the flash of light would return from the other direction.

 

[marcus]

Maybe someday a much more precise measurement of spatial curvature might be made and the 95% confidence interval for the curvature number might be all on the positive side of zero like 0.0001 < |Ω_k| < 0.0004
So then infinite radius of curvature would be excluded with 95% confidence and we would have an UPPER bound on it, as well as a lower bound.
The square root of 0.0001 is 0.01, so whatever the Hubble radius is at that time, say it is 14.6 Gly, we would divide that by 0.01 to get the upper bound estimate. And divide 14.6 Gly by 0.02 to get the lower bound estimate.

 

[madness]

Thanks Marcus. One question has been bugging me about this. As far as I'm aware, a popular viewpoint is that the universe is flat. To my knowledge, that requires a curvature of exactly zero (for a homogeneous universe). This seems incredibly unlikely, as any minute deviation below or above zero would lead to a hyperbolic or spherical universe, albeit very large. If this is true, how can the flat universe hypothesis be entertained, given that it requires a fine tuning to an infinitely precise degree?

I don't like the argument that the universe can be "approximately flat". Locally, maybe, but globally a sphere and a plane are different objects.