# B What is the size of the observable Universe?

#### HankDorsett

Gold Member
Summary
What is the size of the observable universe and a bit of a rant.
Summary: What is the size of the observable universe and a bit of a rant.

I've only recently jumped down the rabbit hole of physics. A social media post on time dilation four months ago got me hooked. Not only has it been a great way to exercise my brain, some of its discovery has been entertaining. Unfortunately my primary source of understanding came from the internet. At first I accepted whatever showed up from a search, as I learned more I started to questioning those results. I would like to know the scientifically accepted size of the observable universe. I have found answers ranging from 93 billion light years in diameter down to 26.6 billion light years in diameter. Not only is there a large discrepancy between the size, even a novice such as myself is able to dispute a couple fairly easily.

#### phinds

Gold Member
Summary: What is the size of the observable universe and a bit of a rant.

I've only recently jumped down the rabbit hole of physics. A social media post on time dilation four months ago got me hooked. Not only has it been a great way to exercise my brain, some of its discovery has been entertaining. Unfortunately my primary source of understanding came from the internet. At first I accepted whatever showed up from a search, as I learned more I started to questioning those results. I would like to know the scientifically accepted size of the observable universe. I have found answers ranging from 93 billion light years in diameter down to 26.6 billion light years in diameter. Not only is there a large discrepancy between the size, even a novice such as myself is able to dispute a couple fairly easily.
The confusion probably arises out of the fact that "now" is an English language term that is not well defined in cosmology. You have to be considerably more specific. If that sounds weird to you, well ... welcome to cosmology. Keep reading and you'll get it after a while. You have to be sure you understand just what it is that is being described as having some specific diameter.

The "accepted" figure is 93 billion light years in diameter "now" but the objects that emitted the light that we say is that far away "now" were nowhere near that far away when they emitted the light.

#### HankDorsett

Gold Member
The confusion probably arises out of the fact that "now" is an English language term that is not well defined in cosmology. You have to be considerably more specific. If that sounds weird to you, well ... welcome to cosmology. Keep reading and you'll get it after a while. You have to be sure you understand just what it is that is being described as having some specific diameter.

The "accepted" figure is 93 billion light years in diameter "now" but the objects that emitted the light that we say is that far away "now" were nowhere near that far away when they emitted the light.
Please don't take what I'm about to say as hostility, I'm just trying to fully understand this.
93 billion light years is the most prevalent response for this question. Unfortunately, if you stay within the confines of scientific
The confusion probably arises out of the fact that "now" is an English language term that is not well defined in cosmology. You have to be considerably more specific. If that sounds weird to you, well ... welcome to cosmology. Keep reading and you'll get it after a while. You have to be sure you understand just what it is that is being described as having some specific diameter.

The "accepted" figure is 93 billion light years in diameter "now" but the objects that emitted the light that we say is that far away "now" were nowhere near that far away when they emitted the light.
Please don't take what I'm about to say as hostile, I'm just trying to fully understand it.
93 billion light years is the most prevalent answer to this question. Unfortunately, if you stay within the confines of scientific definitions this can't be true. The observable universe is defined as "a spherical region of the universe comprising all matter that can be observed from Earth". Observation is defined as "receiving knowledge of the outside world through our senses, or recording information using scientific tools and instruments". The most distant object we have ever observed is a Galaxy that is estimated to be 13.3 billion light years away. Because of this observation I would say that are proven observable universe is 26.6 billion light years in diameter. The high estimate using Hubble suggest we should be able to see 15 billion light years away, giving us a theoretical observable universe of 30 billion light years in diameter. I believe that 93 billion light year number came from a study that estimated the size of the known universe. The study estimated where the farthest galaxies could be after billions of years of expanding universe. I can't see how this could be considered observable if the only thing we have this far out is an estimated location.

#### Bandersnatch

The subject can be confusing when you first encounter it. I agree with @phinds that you need to be careful and make sure you understand what precisely is meant by each statement you use.

You started well enough with defining observable universe. But further down the post it gets a bit murkier.
Let's go over each content-bearing statement.
The most distant object we have ever observed is a Galaxy that is estimated to be 13.3 billion light years away. Because of this observation I would say that are proven observable universe is 26.6 billion light years in diameter.
The most distant would be the cosmic microwave background radiation. That's just the most distant galaxy, whereas there is quite a bit of space seen further away, at the time when galaxies hadn't yet formed (but filled with gas). However, it's beside the more important point addressed below.
Here we have a citation of distance, but no indication what distance is being used. There is a whole lot of different distance measures used in cosmology, where their use is dictated by certain measurable properties, but doesn't necessarily resemble anything like the everyday meaning of distance.
In particular, the distance cited above is 'light travel time distance'. It is what you get if you multiply the time it took light to arrive to us to be observed times the speed of light. This would give you something very much like the everyday notion of distance, if not for the fact that we don't live in a static universe.
If you imagine an emitter at some initial distance $D_{initial}$ from the observer, sending a light signal in a universe that is not undergoing expansion, then by the time $t$ the signal arrives, it will have travelled $D_{travel}=ct$. The object at the moment of reception is at distance $D_{final}$. Because the universe is static, all distances are equal: $D_{initial}=D_{travel}=D_{final}$.

But, if the space, through which the light signal is travelling, is expanding, these distances will differ. After emission at $D_{initial}$, the signal begins to approach the observer, while the emitter is receding from its initial spot. After time $t=D_{travel}/c$ it arrives. By that time, the emitter has managed to recede to $D_{final}$. Now, $D_{initial}<D_{travel}<D_{final}$.
So, if asked what is the distance to the observed object, we can say it is either of the distances, and each will have a different numerical value, but also mean different things. $D_{initial}$ is where it was at emission, $D_{final}$ is where it is now (in the sense that, if you could stop the expansion and take a measuring stick, that's where you'd find it). The distance $D_{travel}$ doesn't have any concrete physical meaning that'd map to our everyday understanding. The emitter neither was nor is at that distance.

So, after this long-winded exposition, the point would be that one should not use the light travel time distance as a measure of the size of the observable universe, because it's essentially meaningless, if convenient in some scientific contexts.

It's also, perhaps, important to note that the light travel distance is not a direct observable - you can't ask a photon how long it's been going for. Neither are any other of the distances. The main direct observable is the redshift, with all distances derived with the use of cosmological models. So, providing you do want to make a statement on the size of the observable universe, you do have to settle on a derived value.

The high estimate using Hubble suggest we should be able to see 15 billion light years away, giving us a theoretical observable universe of 30 billion light years in diameter.
Now, what do you mean by that, exactly? Is this the high estimate for the light travel time distance? Using Hubble what? The HST? That's used for all cosmological observations, together with other instruments. The error bars on the age of the universe (so, also the light travel time distance) are not reaching the 15 Gyr mark.
Or, do you mean Hubble law? Since you can arrive at a number resembling in meaning the age of the universe, that close to 15 Gyr (14.5-ish) using its inverse and a lower estimate for the Hubble constant. That'd be a whole new kettle of fish, however, since again, there's no sense in which the farthest observable objects are at 15 Glyr, nor is the universe in any sense 15 Gyr old.

I believe that 93 billion light year number came from a study that estimated the size of the known universe. The study estimated where the farthest galaxies could be after billions of years of expanding universe. I can't see how this could be considered observable if the only thing we have this far out is an estimated location.
That's precisely the meaning of the reported size. As explained earlier, it's the $D_{final}$ distance.
Now, you could argue, that you'd rather use the $D_{initial}$, in which case the universe would be some 88 million light years across. But that seems even more conceptually problematic, as I think you'd agree. The $D_{travel}$ has no physical meaning, and as such is the worst measure to use.
Whereas $D_{final}$ does map, at least partially, to what we mean by where something is. In particular, you can modify the question, and instead of 'how far is the object I see after time $t$ since emission' you can ask: 'how far did my signal travel to after time $t$ since emission' - which is the same number.
(edit: on a second thought, this last bit below is ambiguous, without introducing comoving coordinates - please ignore it) And finally, $D_{final}$ has a technical meaning that maps onto the definition of observability - it's the spatial extent of the base of the observer's light cone, as drawn in an expanding space = the size of the causal patch around the observer.

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#### phinds

Gold Member
Please don't take what I'm about to say as hostile, I'm just trying to fully understand it.
I didn't get anything hostile. That's a feeling and we are not talking about feelings here, we are talking about scientific facts. As @Bandersnatch 's post should have convinced you by now, your issue really is just that you have not studied the whole issue well enough to understand it fully, but I think you are well on your way. Just keep reading and studying.

#### HankDorsett

Gold Member
I didn't get anything hostile. That's a feeling and we are not talking about feelings here, we are talking about scientific facts. As @Bandersnatch 's post should have convinced you by now, your issue really is just that you have not studied the whole issue well enough to understand it fully, but I think you are well on your way. Just keep reading and studying.
I guess I'm too used to the social media world where people take any level of disagreement as a personal attack. One of my big issues was using the internet as a source for information. now that I found this forum I should be able to find more accurate information.

#### HankDorsett

Gold Member
The subject can be confusing when you first encounter it. I agree with @phinds that you need to be careful and make sure you understand what precisely is meant by each statement you use.

You started well enough with defining observable universe. But further down the post it gets a bit murkier.
Let's go over each content-bearing statement.

The most distant would be the cosmic microwave background radiation. That's just the most distant galaxy, whereas there is quite a bit of space seen further away, at the time when galaxies hadn't yet formed (but filled with gas). However, it's beside the more important point addressed below.
Here we have a citation of distance, but no indication what distance is being used. There is a whole lot of different distance measures used in cosmology, where their use is dictated by certain measurable properties, but doesn't necessarily resemble anything like the everyday meaning of distance.
In particular, the distance cited above is 'light travel time distance'. It is what you get if you multiply the time it took light to arrive to us to be observed times the speed of light. This would give you something very much like the everyday notion of distance, if not for the fact that we don't live in a static universe.
If you imagine an emitter at some initial distance $D_{initial}$ from the observer, sending a light signal in a universe that is not undergoing expansion, then by the time $t$ the signal arrives, it will have travelled $D_{travel}=ct$. The object at the moment of reception is at distance $D_{final}$. Because the universe is static, all distances are equal: $D_{initial}=D_{travel}=D_{final}$.

But, if the space, through which the light signal is travelling, is expanding, these distances will differ. After emission at $D_{initial}$, the signal begins to approach the observer, while the emitter is receding from its initial spot. After time $t=D_{travel}/c$ it arrives. By that time, the emitter has managed to recede to $D_{final}$. Now, $D_{initial}<D_{travel}<D_{final}$.
So, if asked what is the distance to the observed object, we can say it is either of the distances, and each will have a different numerical value, but also mean different things. $D_{initial}$ is where it was at emission, $D_{final}$ is where it is now (in the sense that, if you could stop the expansion and take a measuring stick, that's where you'd find it). The distance $D_{travel}$ doesn't have any concrete physical meaning that'd map to our everyday understanding. The emitter neither was nor is at that distance.

So, after this long-winded exposition, the point would be that one should not use the light travel time distance as a measure of the size of the observable universe, because it's essentially meaningless, if convenient in some scientific contexts.

It's also, perhaps, important to note that the light travel distance is not a direct observable - you can't ask a photon how long it's been going for. Neither are any other of the distances. The main direct observable is the redshift, with all distances derived with the use of cosmological models. So, providing you do want to make a statement on the size of the observable universe, you do have to settle on a derived value.

Now, what do you mean by that, exactly? Is this the high estimate for the light travel time distance? Using Hubble what? The HST? That's used for all cosmological observations, together with other instruments. The error bars on the age of the universe (so, also the light travel time distance) are not reaching the 15 Gyr mark.
Or, do you mean Hubble law? Since you can arrive at a number resembling in meaning the age of the universe, that close to 15 Gyr (14.5-ish) using its inverse and a lower estimate for the Hubble constant. That'd be a whole new kettle of fish, however, since again, there's no sense in which the farthest observable objects are at 15 Glyr, nor is the universe in any sense 15 Gyr old.

That's precisely the meaning of the reported size. As explained earlier, it's the $D_{final}$ distance.
Now, you could argue, that you'd rather use the $D_{initial}$, in which case the universe would be some 88 million light years across. But that seems even more conceptually problematic, as I think you'd agree. The $D_{travel}$ has no physical meaning, and as such is the worst measure to use.
Whereas $D_{final}$ does map, at least partially, to what we mean by where something is. In particular, you can modify the question, and instead of 'how far is the object I see after time $t$ since emission' you can ask: 'how far did my signal travel to after time $t$ since emission' - which is the same number.
And finally, $D_{final}$ has a technical meaning that maps onto the definition of observability - it's the spatial extent of the base of the observer's light cone, as drawn in an expanding space = the size of the causal patch around the observer.
thanks for posting all of that. Maybe after a few dozen more rereads I'll have some questions.

15 billion Lightyear Hubble part
I came across an article that gave me this information. It's reasoning stated that because Hubble is able to see so far out into the universe it is able to see light from galaxies that hasn't had a chance to reach Earth yet. they claim to take an account how long it took a Galaxy to form as well as how far light can travel in the expanding universe.

Staff Emeritus
Hubble is able to see so far out into the universe it is able to see light from galaxies that hasn't had a chance to reach Earth yet.
That can't be right. The Hubble's job is to observe the light that has reached Earth.

#### Bandersnatch

It's reasoning stated that because Hubble is able to see so far out into the universe it is able to see light from galaxies that hasn't had a chance to reach Earth yet.
That's impossible.

#### phinds

Gold Member
I came across an article that gave me this information. It's reasoning stated that because Hubble is able to see so far out into the universe it is able to see light from galaxies that hasn't had a chance to reach Earth yet. they claim to take an account how long it took a Galaxy to form as well as how far light can travel in the expanding universe.
As has already been pointed out, that's obviously a contradiction in terms. The observable universe is called that because that's what it IS ... what we can observe. Anything outside cannot be observed. We can already see further back than the formation of any large scale structures such as stars/planets, etc. The earliest/farthest thing we can see is called the Cosmic Microwave Background, aka the Surface of Last Scattering and that happened about 400,000 years after the singularity. It's what is "now" about 47billion light years from us in all directions.

#### russ_watters

Mentor
The most distant object we have ever observed is a Galaxy that is estimated to be 13.3 billion light years away. Because of this observation I would say that are proven observable universe is 26.6 billion light years in diameter.
You haven't actually said what logic makes you think this, but I'll take a guess; If we look to our left and see objects 13.3 bly away and see the same to our right, that's 13.3+13.3=26.6 bly. Right? Is that what you were thinking?

This logic does not account for those objects moving after they sent that light toward us.

#### HankDorsett

Gold Member
it looks like the dumbing-down of some of this information for public consumption has caused me to build up an incorrect understanding.

#### phinds

Gold Member
it looks like the dumbing-down of some of this information for public consumption has caused me to build up an incorrect understanding.
TOTALLY common and not your fault at all. We spend a LOT of time here on PF debunking "facts" that people have "learned" via pop-science presentation, both TV and books.

#### Bystander

Homework Helper
Gold Member
TOTALLY common and not your fault at all. We spend a LOT of time here on PF debunking "facts" that people have "learned" via pop-science presentation, both TV and books.
++10, "...to infinity, and beyond," or whatever Buzz Lightyear's trademark saying happens to be.

#### ScalarPotato

You haven't actually said what logic makes you think this, but I'll take a guess; If we look to our left and see objects 13.3 bly away and see the same to our right, that's 13.3+13.3=26.6 bly. Right? Is that what you were thinking?

This logic does not account for those objects moving after they sent that light toward us.
I am at a loss here.
What is your definition of the word "observable" and your definition of the word "universe"?

#### russ_watters

Mentor
I am at a loss here.
What is your definition of the word "observable"
What we can observe.
and your definition of the word "universe"?
Everything there is.

I'll be disappointed if this is a definitions issue.

#### ScalarPotato

What we can observe.

Everything there is.

I'll be disappointed if this is a definitions issue.
Sorry for any disappointment.
The OP asked what would be the "scientifically accepted size of the observable universe."
There can be only one interpretation: farthest possible scientifically observed raw data of some sort.
Not "observed diameter plus assumed extra diameter due to being older now.", or so it seems to me.
Do you see why I am confused? Your words are ambiguous and where is a current published standard that you could point to as being authoritative?

#### russ_watters

Mentor
Sorry for any disappointment.
The OP asked what would be the "scientifically accepted size of the observable universe."
There can be only one interpretation: farthest possible scientifically observed raw data of some sort.
Not "observed diameter plus assumed extra diameter due to being older now.", or so it seems to me.
Do you see why I am confused? Your words are ambiguous...
No, I don't see why this is difficult. Consider this:

A truck drives past you at 10m/s. When it is 10m away, someone in the back of the truck throws a ball to you at 20m/s with respect to the truck. You catch the ball.

How far did the ball fly in your reference frame.?
How far away is the truck when you catch the ball?

This should not be a difficult issue to grasp.
where is a current published standard that you could point to as being authoritative?
I don't understand what you are asking for.

In any case, we aren't psychics here. You will need to tell us - explicitly - what your issue is. Just expressing incredulity isn't enough for us to figure out what your issue is and enable us to help you.

#### russ_watters

Mentor
Arright, so when I google this question, every one of the first 10 hits gives me the correct(accepted) answer (unless I missed one; I'm on my phone). There is no controversy and no confusion between sources. So this issue should not exist. So what's going on - did you follow the OP here to argue this? OP, where are you getting this issue from?

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#### Bandersnatch

The OP asked what would be the "scientifically accepted size of the observable universe."
There can be only one interpretation: farthest possible scientifically observed raw data of some sort.
Not "observed diameter plus assumed extra diameter due to being older now."
The issue here is that when talking about 'farthest observed data' or 'observed diameter' you are talking about distances that are 1) ambiguous, 2) derived.
The OP had the same issue, which I tried to address in my long-winded post (#4).
Tl;dr;
The observed quantity is not any kind of distance, but the redshift. It carries with itself information about a number of distances, some more physically meaningful than others, that can be extracted with the use of an expansion model.
In particular, it's possible to extract information about where the object was at emission, or where the object is now. It's our decision to report the size of the observable universe as it was then or as it is now.
Arguably, the latter is more resembling of the everyday concept of 'size' than the former, so it stands to reason it is used when reporting the size of the observable universe.
This becomes a bit more apparent if we invert the emitter/observer and have our spot in the universe be the emitter, while some alien in a faraway galaxy is the observer. There were some physical processes occurring at our location in the early stages of the universe that are currently observed by some aliens that are now at a distance of 46 Glyr. They can see our spot despite being 46 Glyr away, so it's a fair thing to say that the observable universe is 46 Glyr in radius.

In any case, reporting the distance now is the convention that has been adopted.

#### mfb

Mentor
The OP asked what would be the "scientifically accepted size of the observable universe."
There can be only one interpretation: farthest possible scientifically observed raw data of some sort.
All measurements humans have ever done have been done in the Solar System (a bit of a stretch with the Voyager probes, but let's ignore that). By your interpretation we can't say the universe is larger than that?

Obviously not. We use our measurements of more distant objects to determine their distance - at the time of emission of the signal and also at the current time. That's what leads to the 46 billion light years.
Do you see why I am confused? Your words are ambiguous and where is a current published standard that you could point to as being authoritative?
Every publication about cosmology uses "observable universe" in that way. You can search arXiv for "observable universe" to get a long list. There is nothing ambiguous about it.

#### James Demers

Keeping it as simple as possible, and ignoring Einstein's eye-roll, here's the executive summary:

The most distant anything we can observe is the cosmic microwave background radiation. The red shift suggests that the light has been traveling for 13.8 billion years. 27.6 billion light years would then be the diameter of the observable universe ... if the universe had been standing still all that time. Which, of course, it hasn't.
The value of 93 billion light years takes into account how much the universe has expanded while the CMB radiation was in transit to our instruments.

#### Grinkle

Gold Member
There can be only one interpretation: farthest possible scientifically observed raw data of some sort.
Not "observed diameter plus assumed extra diameter due to being older now."
Replace the word assumed with the word calculated. You label expansion an assumption because you don't understand refrence beacons and doppler shift. Some of the observed light comes from objects that we know from physics emitted the light at a higher frequency than we are measuring so we are observing the expansion and calculating its rate, not assuming it. The expansion is as direct an observation coming directly from raw data as any other cosmological conclusion regarding the size of the OU. Its a mistake to demote anything you don't immediately intuitively understand to an assumption on the part of others.

Such reasoning might as well be used to conclude that the earth orbiting the sun is an assumption, and direct observation shows clearly that the earth is the center of the universe.

#### kimbyd

Gold Member
2018 Award
it looks like the dumbing-down of some of this information for public consumption has caused me to build up an incorrect understanding.
There's that, but there's also the fact that this stuff is just inherently confusing, because curved space-time is a very difficult thing to wrap your head around. And the question of how big the observable universe is is inherently tied to the curvature of space-time: the limit of the observable universe is a horizon very much akin to the horizon of the Earth, a horizon that exists precisely because of the curvature of the Earth.

And the distance to that horizon is not a well-defined thing with a single answer. To understand why, consider again the surface of the Earth. Imagine a point on the opposite side of the Earth from you. How far is that point away? Do you measure the distance using a straight line through the Earth? Or do you measure it using the shortest path along the surface of the Earth (the Great Circle Distance)? Or do you measure it using travel distance given some modes of transportation?

Each estimate of distance is correct in its own way, and each is useful in a certain context. Travel distance is the most useful for most people in most situations. Great Circle distance may be the most useful if you're attempting to do something like cartography or climate modeling, or estimating flight paths before taking weather into account.

When it comes to large distances in our universe, such ambiguities are an essential part of the problem. There is a definite answer once you've agreed on what type of distance you're talking about. But the type of distance is just as important as the answer itself.

#### PeterDonis

Mentor
Do you measure the distance using a straight line through the Earth?
Just for clarification, this particular distance in the Earth case does not have an analogue in the case of the universe; there is no way to go "through" anything to short cut the distance in the universe.

"What is the size of the observable Universe?"

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