# What is the current radius of the observable universe?

• marcus
In summary: XIn summary, the most commonly used indices for measuring distance in cosmology are redshift (z) and "comoving distance". According to the prevailing models, the comoving distance is measured from rest with respect to the CMB and is used in Hubble's law to relate distance to velocity. Other types of distance, such as angular distance and luminosity distance, are also used but may be more difficult to determine. It is the standard expert view that parts of the observable universe are currently receding faster than the speed of light, as seen in the example of a quasar with a redshift of 6.4. This can be calculated using the cosmology calculator on Wright's website and is a characteristic built into the prevailing

## How big is the observable universe (assuming age is 14 billion years)

• ### [8)] none of the above

• Total voters
11
marcus
Gold Member
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How far away are the most distance objects we can see?

What is currently the volume of space that we can study with the light that is reaching us?

You might want to look at this brief Cosmology FAQ paragraph:

http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN

*******footnote stuff, background on distance scales used****

Cosmologists use several different indicators of distance and
for a discussion of the various sorts of distance, as well as
a Javascript calculator that converts between them (if you specify
what assumptions you are making about the model), see:

http://www.astro.ucla.edu/~wright/cosmo_02.htm

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

Among the most commonly used indices are redshift (z)
and "comoving distance".

The latter is measured at the present from rest with respect to the CMB and it is the type of distance that works in the
Hubble law relating distance to velocity

v = H0 D

the present comoving distance to an object multiplied by the
current value of the Hubble parameter is equal to the present radial comoving velocity

Other types of distance are "angular distance" (angular smallness of an object of known size) and "luminosity distance"
(dimness of a source of known brightness) and "light travel time".
The last does not work in the Hubble law and may be difficult to determine because different parts of the light's path have undergone different amounts of stretching---the travel time is hard to relate consistently to other measures of distance. But it is one of the indices that is calcuated by the "Cosmo Calculator" at Ned Wright's site.

The edge of the universe expanding at the speed of light should be a distance r = c/H if you just analyze H=dr/rdt for r with dr/dt=c.

The edge of the universe expanding at the speed of light should be a distance r = c/H if you just analyze H=dr/rdt for r with dr/dt=c.

Why should the edge of the obs. universe be receding from us at only the speed of light?

In GR lots of things go faster than light (the limit only belongs
to SR and very local contexts)

A quasar has been observed with z=6.4

According to the most standard picture of things (Astro 101)
this quasar is currently receding at twice the speed of light.
And it is certainly part of the observable universe. Indeed we can see well past redshift 6.4!

Please explain why you say these things!

god save the empire and Albert Einstein too

Originally posted by marcus
Why should the edge of the obs. universe be receding from us at only the speed of light?
Because, for a location to be observable, information must have traveled to us from that location. Information cannot propagate faster than light.
In GR lots of things go faster than light (the limit only belongs
to SR and very local contexts)
I'm not quite sure you understand general relativity...
According to the most standard picture of things (Astro 101)
this quasar is currently receding at twice the speed of light.
Perhaps you should double-check this conclusion.

- Warren

Chroot has done it again!

You are off-base Chroot, the simplest way to get up to speed would probably be to look at John Baez gen rel tutorial and
Ned Wright's cosmology tutorial. I will try to get some links for you.

Just for refs here is what you said:

******************

quote:
--------------------------------------------------------------------------------
Originally posted by marcus
Why should the edge of the obs. universe be receding from us at only the speed of light?
--------------------------------------------------------------------------------

Because, for a location to be observable, information must have traveled to us from that location. Information cannot propagate faster than light.

quote:
--------------------------------------------------------------------------------
In GR lots of things go faster than light (the limit only belongs
to SR and very local contexts)
--------------------------------------------------------------------------------

I'm not quite sure you understand general relativity...

quote:
--------------------------------------------------------------------------------
According to the most standard picture of things (Astro 101)
this quasar is currently receding at twice the speed of light.
--------------------------------------------------------------------------------

Perhaps you should double-check this conclusion.

- Warren

********************

It is not my conclusion. It is the standard expert view
that I am just relaying. I have double-checked it
because when first encountered it is mindboggling
that parts of the U are currently receding faster than light.
I have repeatedly checked it and (counterintuitively enough)
it is the case----i.e. a characteristic built into the prevailing models.

I don't want to argue because it is not my baby-- it's just the ordinary educated view---but I will try to find you some URLs.

A URL for Chroot

Go to Wright's javascript cosmology calculator

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

put in z = 6.4 and press "flat"

(a quasar with redshift 6.4 was observed last year by
Bob Becker at UC Davis et al. so you are finding the
comoving distance to that particular object, with the
assumption that the universe is flat)

The calculator will go:

"The comoving radial distance, which goes into Hubble's law, is 8589.1 Mpc or 28.014 Gly."

Now hubbles law is just v = H0 D
where D is the comoving distance and v is the speed of recession.

So just plug in 28 billion LY and you will get that the speed
is 600 thousand kilometers of second-----twice the speed of light.

that is the current speed of recession of that part of the observable universe where that particular quasar lives

explanations can be found aplenty in the Usenet Physics FAQ
and various tutorials: Wright's and others.

Marcus I have to call you on this

A Z=6.4 doesn't mean the Quasar is moving at twice the speed of light, it means it has two units of Velocity Parameter/Rapidity. There is a hyperbolic relationship between Rapidity and Velocity. Rapidity is expressed in units of C but the true velocity is the hyperbolic assymtote of the Rapidity.

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Originally posted by Tyger
A Z=6.4 doesn't mean the Quasar is moving at twice the speed of light, it means it has two units of Velocity Parameter/Rapidity. There is a hyperbolic relationship between Rapidity and Velocity. Raapidity is expressed in units of C but the true velocity is the hyperbolic assymtote of the Rapidity.
Well said. I didn't actually feel like trying to explain it.. marcus tends to be rather full of himself.

- Warren

Why should the edge of the obs. universe be receding from us at only the speed of light?
Simply because space that is outside the radius at which the expansion = c has "velocity" > c assuming homogeneous space expanding everywhere and thus is unobservable, like the inside of a black hole.

*edit
tyler is right if v=c then z=infinity

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Simply because space that is outside the radius at which the expansion = c has "velocity" > c assuming homogeneous space expanding everywhere and thus is unobservable, like the inside of a black hole.

*edit
tyler is right if v=c then z=infinity

Actually, in the course of time, do we see more or less of the observable universe? Or is our horizon of observation always limited to a fixed part of the material world (even though the size of it increases in time)

In other words can material objects which previously were not within our horizon, become visible one day? Can material objects which now are visible to us, become invisble one day?

And another thing, I would like to propose a new outlook on the universe in total, founded on the assumption that space itself does not in anyway expand (just by defining the unit of measurement to be exactly proportional to the expansion of space, provided that the expansion rate is a global feauture of the universe).

Some may say, it is a weird idea or even disallowed by Nature.
However a well established principle of physics and physics laws is that physics does not depend on our choice of measuring units.
This is a valid proposition, and could only be rejected if one assumed that nature comes up with a preferred set of measuring units, which are hold to be constants of Nature.

The simple thought of using a measuring unit for length that is proportional to the overall expansion of space, and taken the speed of light to be constant, means also that the time unit must be proportional to that.

In fact that means that the age of the universe is infinite, and there was no Big Bang singularity at all.

However a measuring unit for length that is proportional to the space expansion, does mean - while on one side it excludes the phenomena of expansion of space - on the other side it introduces a new, yet unexplained phenomena, that of material contraction, within all material objects (from galaxies to atoms and below).

This new outlook presents us with another contradiction.
While on one side removing the "beginning of time", making time in fact of infinite extend in both directions, it introduces the fact that space is to be thougt of finite extend (always the same size).

No matter how we look at it, and independend of our units of measurement, the universe as a whole will always present us a contradiction.

However, the fact that within all forms of material existence, contradictions are inherently there, is an unavoidable property of material existence, because it's the only way in which matter can exist. Without contradiction matter would not exist, and that would cause an even more profound contradiction, namely that nothing would exist.

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Originally posted by heusdens

And another thing, I would like to propose a new outlook on the universe in total, founded on the assumption that space itself does not in anyway expand (just by defining the unit of measurement to be exactly proportional to the expansion of space, provided that the expansion rate is a global feauture of the universe).

Some may say, it is a weird idea or even disallowed by Nature.
However a well established principle of physics and physics laws is that physics does not depend on our choice of measuring units.
This is a valid proposition, and could only be rejected if one assumed that nature comes up with a preferred set of measuring units, which are hold to be constants of Nature.

The simple thought of using a measuring unit for length that is proportional to the overall expansion of space, and taken the speed of light to be constant, means also that the time unit must be proportional to that.

In fact that means that the age of the universe is infinite, and there was no Big Bang singularity at all.

However a measuring unit for length that is proportional to the space expansion, does mean - while on one side it excludes the phenomena of expansion of space - on the other side it introduces a new, yet unexplained phenomena, that of material contraction, within all material objects (from galaxies to atoms and below).

This new outlook presents us with another contradiction.
While on one side removing the "beginning of time", making time in fact of infinite extend in both directions, it introduces the fact that space is to be thougt of finite extend (always the same size).

No matter how we look at it, and independend of our units of measurement, the universe as a whole will always present us a contradiction.

In Quantum Mechanics a displacement of our coordinates to the left is equivalent to a displacement of the system to the right. They are physically and mathematically indistinguishable interpretations. Since the represntation of the Universe expanding while matter remains the same size is a mathematical convention I don't see why we couldn't view the space of the Universe as remaining the same size while the matter in it shrinks.

However I don't think that can be used to infer that there was no "beginning of time".

In my opinion we just don't know enough experimentally or theoretically to close the books on the shape and future history of the Universe. We don't know where the Matter in it came from, or even whether it might be being produced today. Fresh Hydrogen from deeper space is moving into spiral galaxies along the arms, that is what fuels new star formation. We don't know if various "constants" are changing with time, throwing our calculations of past history off.

We have to always contend with the fact that Nature has a bigger and more precise imagination than we inside observers of her have.

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Originally posted by Tyger
In Quantum Mechanics a displacement of our coordinates to the left is equivalent to a displacement of the system to the right. They are physically and mathematically indistinguishable interpretations. Since the represntation of the Universe expanding while matter remains the same size is a mathematical convention I don't see why we couldn't view the space of the Universe as remaining the same size while the matter in it shrinks.

However I don't think that can be used to infer that there was no "beginning of time".

When we change our length unit to that comprising the expansion of space, and when considering the speed of light to be constant, this necessitates us to change the unit of time as well. Seen from the old units of time and length, the new units of time and space were both in a proportinal way smaller in the past. When measured in the new time and length units, it follows that the size of the universe is constant and that the age of the universe is infinite.

It's a simple conclusion. But not necessrarily true, but just legimated on the basis (assumption) of the validity of the new length and time units. But it is argued that this or that system of measuring units, are in fact "equal", which means we can not make absolute judgement about that, only relative ones. We have to take into account that one truth (based on one system of measuring units) contradicts another (based on another system of measuring units).
That is just what the world is.

And here is one more analogy from geometry, to accommodate this idea of a universe being finite in time in one time unit, and infinite in time in another time unit...

Think of paralle lines. In flat eucledian space, the lines never intersect and extend to the infinite. In non-flat space, the lines wlll intersect within a finite distance however. I hope this can make you bridge these opposing thougths.

In my opinion we just don't know enough experimentally or theoretically to close the books on the shape and future history of the Universe. We don't know where the Matter in it came from, or even whether it might be being produced today.

Matter (using the philosophical term matter) can not be created or destroyed, but only be transformed. But notice that I use matter to denote all forms of matter (particles, waves, energy, fields), not just the physical matter.

We have to always contend with the fact that Nature has a bigger and more precise imagination than we inside observers of her have.

We can imagine that Nature can imagine, but I really doubt if Nature itself (apart from us) can imagine anything at all. Nature is just the reality outside of our imagination and independend of it, and our imaginations are the projections of Nature/reality in our brains.

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Originally posted by chroot
Since you were smart enough to find Wright's page, you should have been smart enough to find his FAQ.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN

- Warren

People, check out this page that chroot refers to! It is very instructive. In fact chroot I am rather familiar with this one of
Wright's FAQ and not long ago was discussing it in another thread at PF with someone else. What you point to begins:

"If the Universe is only 10 billion years old, how can we see objects that are now 30 billion light years away?"

"When talking about the distance of a moving object, we mean the spatial separation NOW, with the positions of both objects specified at the current time. In an expanding Universe this distance NOW is larger than the speed of light times the light travel time due to the increase of separations between objects as the Universe expands. This is not due to any change in the units of space and time, but just caused by things being farther apart now than they used to be..."

Wright's tutorial and FAQ contain plenty of references to the fact that parts of the observable universe are receding from us faster than c----this is routine. Don't see how this FAQ reference supports your claims---tends more to help dismiss them."

Someone should do a tutorial at PF on the Hubble law and how the Hubble law distance is defined

Actually, in the course of time, do we see more or less of the observable universe?
A star that is near the edge of the visible universe will have global velocity wrt us as well as local velocity, so might escape after time if local velocity is < global.

Originally posted by Tyger
A Z=6.4 doesn't mean the Quasar is moving at twice the speed of light, it means it has two units of Velocity Parameter/Rapidity. There is a hyperbolic relationship between Rapidity and Velocity. Rapidity is expressed in units of C but the true velocity is the hyperbolic assymtote of the Rapidity.

Hello Tyger,
Have a look at FAQ "Can objects move away from us faster than the speed of light?"

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

Also you might find part 2 of Wright's cosmology tutorial interesting. The four types of distance are discussed including the "comoving" distance that works in the Hubble law.

http://www.astro.ucla.edu/~wright/cosmo_02.htm

Did you actually try out the calculator?
This is important. Please try it.
Based on the best model we have at present if you put in z=6.4 it will calculate the "radial comoving distance that goes into the Hubble law" as 28 billion LY.
THAT is what tells us that the rate that space around the quasar is receding from us is 2c at the present time.
It is something that must be calculated---when you use the calculator leave the parameters that he put in it alone and just press the "flat" button.

Your answer suggests you are confusing this with the special relativity doppler formula. In SR there are no velocities greater than c and IIRC you can get beta from w=z+1 by the inverse doppler
formula
beta = (w2-1)/ (w2+1)
If you think THIS is what is involved you are missing the point.
It sounded like you thought I didnt know this "hyperbolic" formula or whatever and that you were telling me about it.
Indeed this formula never gives a beta bigger than one!
But that is beside the point.

The situation in GR is different and it is routine for parts of the observable universe to be currently receding at speeds greater than c and the tutorials on the web make this point over and over again. It does not violate SR, which is a local theory.

BTW you are right to say z=6.4 does not MEAN that the quasar is receeding at 2c. What it means is what it says, redshift 6.4. But from that redshift which concerns some light emitted maybe 11 or 12 billion years ago one can, using what is currently known about the universe, CALCULATE where the quasar is now. And how fast is is currently receding, or if you prefer to think of it as sitting still, how fast the space it is sitting in is receding from us.

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marcus,

You really have no idea what you're talking about.

- Warren

Quote by heusdens

We can imagine that Nature can imagine, but I really doubt if Nature itself (apart from us) can imagine anything at all. Nature is just the reality outside of our imagination and independend of it, and our imaginations are the projections of Nature/reality in our brains.

Nature imagined you!

OK Marcus

I'm beginning to see what you're talking about. Near a gravitating body the space around it is being drawn in, in effect it is shrinking around the body. But on the largest scale space itself is expanding, just the opposite of the shrinking. And that has to be taken into account in our calculations. Whereas I was looking at space as being essentially flat with just the objects in it moving apart. That is certainly a different picture.

Tyger thanks for the kind words

Originally posted by Tyger
I'm beginning to see what you're talking about. Near a gravitating body the space around it is being drawn in, in effect it is shrinking around the body. But on the largest scale space itself is expanding, just the opposite of the shrinking. And that has to be taken into account in our calculations. Whereas I was looking at space as being essentially flat with just the objects in it moving apart. That is certainly a different picture.

I am glad you are feeling like you understand things better.
The root cause of the misunderstanding is the existence of two different ideas of distance.

Cosmologists like to use the "comoving distance" that works with the Hubble law and refers to measurement by observers who are at rest with respect to the CMB. It turns out to be a good clear idea of distance.

Journalists like to use "light travel time" as an idea of distance but this has many pitfalls and leads to confusion. It doesn't measure distance between things in the present. And different parts of the light's path get stretched out by different amounts (early parts have time to be stretched more). so it is a fickle unreliable disaster as a distance measure.

So you get FAQ by for instance Ned Wright who teaches cosmology and who explains the good kind of distance---FAQ like
"if the age of the universe is 13 billion Y then how come we can see things that are 39 billion LY away?" He does it with 10 and 30 but it would be more realistic to say 13 and 39. And he
explains "comoving distance" in quite a bit of detail. It is
distance IN THE PRESENT from the standpoint of observers who are at rest with respect to the CMB i.e. to the expansion of space.
In cosmology there is a preferred frame----different from SR where there is no preferred frame.

And he explains why it is that the current boundary of the observable universe is receding at 3 times the speed of light and so on. It is pretty simple once you get used to it.

Like, a quasar that we see with redshift 6.4 was not so far
away THEN when the light left it and was not receding so fast THEN, but by now, in the present moment, it is 28 billion LY away and is receding at twice the speed of light.

And that is a fairly routine speed for some portion of space to be receding. The speed of expansion of space is PROPORTIONAL to distance---that is what the Hubble Law v=HD says. So since
expansion has that linearity or proportionality there MUST be lots of space receding from us at speeds greater than c or 2c, etc.

I don't know why people sqwawk so much when one says this.

I see.
so if space is expanding like H = dr/rdt then the R in the present moment would be R=Roev/c ?

I see.
so if space is expanding like H = dr/rdt then the R in the present moment would be R=Roev/c ?

Hello "2GM/c2"

Would it be all right to use the letter D to stand for the
distance to some object, like a galaxy?

I am used to seeing the Hubble law written v=H0D

the subscript zero means "value at the present time"
v is the comoving radial velocity at present
D is the distance at present (must be the comoving distance not the light travel time distance, for the law to be valid)

I am used to seeing R, in these contexts, meaning not the distance to an object but a scale factor that goes into the metric or that indicates "average distance between galaxies".
It serves as an index of the size of the universe (since the universe is infinite one needs some spacing index like average distance between galaxies) to keep track of the expansion.
R0 is the PRESENT value of this size indicator.

And the "a" that one sees in the Friedmann eqns. is a dimensionless version of R, namely R/R0 .

You divide past and future R by the present value and get a number which at the present is one. Then the Friedmann equations take on their usual textbook form.

Is this notation OK with you? Or would you like to use R to be the distance to some object?

Anyway, if I stick to what I'm familiar with for the moment, the Hubble law is v= H0 D, and that (not what you wrote) is the way that current velocity and current distance of objects are related. It is a simple linear relation which is kind of a relief, and (as Wright say) it holds for all distances.

(forgetting about proper motion, which at large redshifts is a small part, just a sort of random fuzz, compared with the main speed of expansion of space)

Marcus - It's unfortunate no one here was able to give you the answer to your question "what is the current radius of the universe".

The answer is: 4 x 10^26 meters

There you have it.

Originally posted by LogicalAtheist
Marcus - It's unfortunate no one here was able to give you the answer to your question "what is the current radius of the universe".

The answer is: 4 x 10^26 meters

There you have it.

This is a charming answer. I am used to thinking of such distances in LY so let me convert your 4E26 meters.

Hmmm a LY is 9.46E15 meters, so you are saying...

Ye gods and little fishes! You are saying

FORTY TWO BILLION LIGHT YEARS!

YES! Measured at the present moment from perspectives at rest relative to the Cosmic Microwave Background, this is indeed the upper limit on the distance of the farthest detectable sources. this is the radius of the observable universe at present.

Tell me how to become an atheist. I will join your church
I am glad to have met you.

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Again this question, on which I heard opposing views.

Our visible universe is known to expand. The question I have is wether this expanding buble of space, that denotes our horizon of vision, always "contains" (that is: visible at some specific point in time, cause the light reaches us) the same amount of matter.
Or in other words, does this expanding bubble as it grows in the course of time show us more galaxies and stars then in the past, or quit opposite, galaxies and stars that were visible once, escape from our horizon, cause they recede from us at speeds > c?

This is an excellent question to have thought to ask.
The future contents of the observable universe depend on what model one choses. Soon after "dark energy" and "accelerating expansion" became popular topics (1998) cosmologists began to point out that with accelerating expansion after a while the observable universe might have only a hundred or so galaxies in it----we would get lonely in other words.

One must be mentally prepared for the expansion rate to change and even to reverse. If the universe begins to contract at some time in the future---a logical possibility---the "bubble" as you call it would get very full of matter and radiation---we would have too much company.

That said, I can answer your question under the simplifying assumption of a flat universe with no cosmological constant (zero "dark energy")----by far the simplest model and until recently the most realistic and widely assumed.

Orthodox cosmologists use a special idea of rest frame---that of an observer at rest with respect to the expansion of the universe---also called the "Hubble flow" (just another name for uniform expansion)----which means at rest with respect to the CMB.

They use the distance definition, and the idea of simultaneity, which belongs to this rest frame. The distance is measured at the present instant of time and is called the "comoving distance".
For an unmathematical but careful definition look in Wright's Cosmology tutorial.

A feature of the tutorial called the Cosmological Calculator will find the comoving distance to things given the redshift in their most recent observation. So if a quasar is observed with redshift z = 6.4 the calculator will tell you the current comoving distance to it.

This is about 27 billion LY, as I recall. Space around that particular quasar is currently receding at about 2c. (This is the standard Hubble law v = H0 D, interpreted in the normal way that cosmologists use the law. Widely misunderstood by outsiders unfortunately.)

Originally posted by heusdens
The question I have is wether this expanding buble of space, that denotes our horizon of vision, always "contains" (that is: visible at some specific point in time, cause the light reaches us) the same amount of matter.

No it does not!

Originally posted by heusdens

Or in other words, does this expanding bubble as it grows in the course of time show us more galaxies and stars then in the past?

Yes! under the simple assumptions about the expansion which i stated.

I have to go, but will get back for more discussion later. Here for reference is your complete post.

Originally posted by heusdens
Again this question, on which I heard opposing views.

Our visible universe is known to expand. The question I have is wether this expanding buble of space, that denotes our horizon of vision, always "contains" (that is: visible at some specific point in time, cause the light reaches us) the same amount of matter.
Or in other words, does this expanding bubble as it grows in the course of time show us more galaxies and stars then in the past, or quit opposite, galaxies and stars that were visible once, escape from our horizon, cause they recede from us at speeds > c?

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a picture of what I'm describing

http://www.astro.ucla.edu/~wright/cosmo_03.htm

and scroll down the page till you come to the paragraph
"Manipulating Space-Time Diagrams"

You will see a picture of our past light-cone
in the "flat" (critical density) zero-Lambda case.
It is a good approximation even though the dark energy term is zero

In the spacetime diagram the observable universe is
PEAR SHAPED going back to the beginning of time.

I am not saying to browse Wright's Tutorial (which you probably already have done, like everybody else I know)
I am pointing to a particular spacetime diagram in a specific paragraph on page 3.

The age of the univere in that diagram is 8 units (these would be units of 1.7 billion years).

You can see the world lines of the other galaxies in it and you can see if you redrew the PEAR for an age of 7 time units it would be a smaller pear and would contain fewer other galaxies!

this shows that the observable universe actually contains more matter as time goes on.

This is not an obvious conclusion but depends on assumptions about the model, so it is a good thing to be asking about.

Originally posted by marcus

http://www.astro.ucla.edu/~wright/cosmo_03.htm

and scroll down the page till you come to the paragraph
"Manipulating Space-Time Diagrams"

You will see a picture of our past light-cone
in the "flat" (critical density) zero-Lambda case.
It is a good approximation even though the dark energy term is zero

In the spacetime diagram the observable universe is
PEAR SHAPED going back to the beginning of time.

I am not saying to browse Wright's Tutorial (which you probably already have done, like everybody else I know)
I am pointing to a particular spacetime diagram in a specific paragraph on page 3.

The age of the univere in that diagram is 8 units (these would be units of 1.7 billion years).

You can see the world lines of the other galaxies in it and you can see if you redrew the PEAR for an age of 7 time units it would be a smaller pear and would contain fewer other galaxies!

this shows that the observable universe actually contains more matter as time goes on.

This is not an obvious conclusion but depends on assumptions about the model, so it is a good thing to be asking about.

This conclusion, followed from this line of thought, I was already aware of. But I ask the question, cause one could think of another line of thought, which implements the opposite, namely because of the fact that the "recession speed" can be bigger then c, which would mean that at some time, far remote objects move out of our horizon.

Is this a valid representation and conclusion, based on the fact that very far remote objects in principle can have recession speeds bigger then c?

Length unit

And here is another issue, related to measuring on larger scale size.

First we denote the fact that from GR it can be stated that space is "expanding" in all parts of space. We do not know exactly the amount of space expansion throughout history (it is asummed now, that the expansion in fact accelerates!), but the assumption is that the rate of expansion at any given time (as measured relative to the Big Bang) is constant throughout space.

The fact that we claim that space expands, is a fact which is based on the choice of measuring unit. The measuring unit we have are based on some fundamental constants (I heard it can be expressed using constants of c, h and perhaps G). In principle thought the choice of the length unit is arbitrary. Of course, anyone agrees that if the length unit would expressed differently, this would not alter any of the physical phenomena and laws, it would just alter numerical results.

But how arbitray is the choice of measuring units? We can of course think of choices of length units, which are wrong. As an example, the distance between Earth and the sun, would not be a good candidate for the length unit. Since we know from the old measuring units, that the distance between the Earth and the sun is not constant. If we choose this distance as the length unit, this would then mean the distance between Earth and the sun would be constant. But at the same time, the radius of Earth and all other objects known to us, would also vary in time, in a periodically way. No known laws of physics could explain this fact, and that just means this choice of measuring unit is invalid.

But what if our length unit would be choosen in such a way, that it does express some fundamental property of nature. As I suggest, the expansion of space itself, could be a derivate for such a length unit. The choice would then be to denote this measuring unit in such a way, as to effectively "remove" the space expansion. The unit of length could be defined as the distance in space of two very distantiated objects, which both are "stationary" in respect to the CMBR (from the anisotropy of the CMBR we can for instance measure our speed and direction relative to the CMBR). Although this length unit would by no means be practical (which in itself is not a problem, but just requires to properly rescale the unit) it also would mean a totally different perspective on physical phenomena and physical law. For instance the phenomena of "space expansion" would not be a phenomena any more. On the other hand, this "new physics" would have to deal with explaining why all material objects (galaxies, stars, atoms, etc) are contracting in the course of time.

As can be stated all other measuring units (time, mass, etc) would also "behave differenly" in this new measuring unit system, and it would effect also the universal constants, of which some might not be a constant.

The only way this idea for a new measuring unit, which is porportional in time with the expansion of space (effectively cancelling the space expansion phenomena), can be invalidated is to state that the length units we currently have, denote fundamental properties of nature, are expressed in universal constants which are known not to change.

But so far as I can understand physcial law myself, the notion of the universal constants, are assumptions, which - although the reasons for stating that they are constants are strong - do not have to conform reality. For instance the value of h, G or even c in the far past could have been different values as now.

Some theoretical physicist in fact are playing with the thought that some fundamental constant might not be fundamental constants alltogether, and which also gives rise to the idea that perhaps in different frames of reference, we need to apply different measuring units. This is for instance the case with the idea of 'Double Relativity' (see https://www.physicsforums.com/showthread.php?s=&threadid=1465").

Although these ideas are not the same as my idea/proposal for redefining the length unit, and with that effectively 'create' a new physcics, alongside with the old physics, it sure means that our current way in which we define measuring units and universal constants, might not be the only way, and might not even be the right way.

My idea about this new length unit, I have not yet thought through completely. It for sure involves a lot, because we need to redefine all of our measuring units, and it would change a lot in our perspective of the universe (notions as 'age' and 'size' of (observable) universe would be quite different) and would urge us to state that all such notions, basically are not in any way fundamental notions, but relative notions (they depend on the choices of measuring unit).
For instance, in the new measuring unit system, since there is no expansion of space, neither a 'Big Bang' phenomena happened, and the age of the universe would be the infinite past.
This can be argued, because when we calculate back to the 'normal' length and time measuring units, the new length and time units (taking speed of light as a constant in the NEW measuring unit system!) would both be expanding in time, which means that further to the past, both measuring units were shorter. So in new time units, the time between now and the big bang denote an infinite amount of time. In effect it would mean that all our references to these things (like the age of the universe) can not be taken as 'absolute' notions, but only 'relative' notions, since it depends on the choise of measuring units.

Perhaps this new vision, based on this new measuring unit for length, is arguably wrong, but as far I have not seen fundamental arguments against it. For instance the argument that the choice of a measuring unit that increases in size in the course of time, is an invalid option, is a way of circular reasoning. Because wether or not something increases in size, is always based on the choice of measuring unit. Based on the new measuring unit, it could be stated that this is not the case, but that our normal measuring unit is shrinking in size. Based on that argument, we could only tell that one of them needed to be incorrect, but we could not tell which one was incorrect.

So the argument then basically comes down to claim that the chosen measuring unit is absolute, and expresses a fundamental property of nature. And of course, that is dependend on some universal properties, which in our measuring units, denote some constants.
But from what do we know that?

I think we can not make any ABSOLUTE claim about that. Which then would lead to the thought that both measuring unit systems have equal validity, even when we know that physical laws and physical phenomena are not identical in both measuring unit systems.

This idea can be thought of as an extention to the theory of relativity, in which not only all measurements are relative, but also the measuring units themselves are relative.

Since most of the time our physical explenations and phenomena we deal with, are on much smaller time and lenth scales as that of the universe, there is of course no reason to leave our normal measuring unit systems and understanding and interpretation thereof.
But for cosmological issues, the new measuring unit system could be a progressive step forwars in understanding the universe.

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Hi heusdens, it is a nice try but doesn't work

I am replying to what you said in previous post:
"But what if our length unit would be choosen in such a way, that it does express some fundamental property of nature. As I suggest, the expansion of space itself, ..."

You have been given a bad misconception from popular accounts and the careless way astronomers talk

The rate that space is expanding is different in different places.
It is uneven.
Uniform expansion is not at all a "fundamental property" of space built into its nature.

When they talk about the expansion rate they mean a kind of temporary average.
The average is only strictly correct for the present moment (t=0) which is why they write the zero subscript on H0.

And it is only a rough estimate gotten by averaging the expansion in various places and directions from us, which rigorously speaking are all different.

The main equations of cosmology---Friedmann's two equations---are boiled down from Einsteins by ASSUMING that the distribution of energy in space is isotropic and homogeneous (same everywhere and in all directions) which it obviously is NOT.

However the Friedmann equations are simple and terribly useful and the work soooooo well! Even though predicated on obviously false assumptions. These equations contain the definition of the Hubble constant----the idealized expansion rate.

We have enough to worry about with the fundamental constants we already have. Please do not suggest that the expansion-rate of space is also a "fundamental constant"!
Compared with other things it is highly changeable.
One should really call it "Hubble parameter" (as some people are starting to do) and not call it Hubble "constant."

But cheers anyway, I sympathize with your interest in scales of measurement and foundations-issues

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Originally posted by marcus
Hi heusdens, it is a nice try but doesn't work

I am replying to what you said in previous post:
"But what if our length unit would be choosen in such a way, that it does express some fundamental property of nature. As I suggest, the expansion of space itself, ..."

You have been given a bad misconception from popular accounts and the careless way astronomers talk

The rate that space is expanding is different in different places.
It is uneven.
Uniform expansion is not at all a "fundamental property" of space built into its nature.

When they talk about the expansion rate they mean a kind of temporary average.
The average is only strictly correct for the present moment (t=0) which is why they write the zero subscript on H0.

And it is only a rough estimate gotten by averaging the expansion in various places and directions from us, which rigorously speaking are all different.

The main equations of cosmology---Friedmann's two equations---are boiled down from Einsteins by ASSUMING that the distribution of energy in space is isotropic and homogeneous (same everywhere and in all directions) which it obviously is NOT.

However the Friedmann equations are simple and terribly useful and the work soooooo well! Even though predicated on obviously false assumptions. These equations contain the definition of the Hubble constant----the idealized expansion rate.

We have enough to worry about with the fundamental constants we already have. Please do not suggest that the expansion-rate of space is also a "fundamental constant"!
Compared with other things it is highly changeable.
One should really call it "Hubble parameter" (as some people are starting to do) and not call it Hubble "constant."

But cheers anyway, I sympathize with your interest in scales of measurement and foundations-issues

That's a good point!

And there is one other thing about the Hubble correlation parameter.
We can only observe this correlation in a very tiny spatial and temporal extent (namely: the temporal and spatial extend in which we know about, or since we do scientific cosmologic observations).

How do we know then that there is a distance - velocity ("virtual" recession speed) relation, it could as well be a time - velocity / virt. reces. speed relation.

For me, the answer is 14 billion y.l. And look what says Alan Guth, the creator of the theory of inflation:
"We find that the universe is expected to be at least 10 to the power of 23 times larger than the observed universe. If the inflationary theory is correct, then the observed universe is only a minute speck in a universe that is many orders of magnitude larger"

Originally posted by meteor
For me, the answer is 14 billion y.l. And look what says Alan Guth, the creator of the theory of inflation:
"We find that the universe is expected to be at least 10 to the power of 23 times larger than the observed universe. If the inflationary theory is correct, then the observed universe is only a minute speck in a universe that is many orders of magnitude larger"

Alan Guth worked out his own version of what is called inflation, based on an idea of the Soviet scientist Starobinsky, end of the '70-ies. This model, about a large scale transformation of matter in the universe, was however too complicated, and in fact did not work.
But it has lead to new attempts, for instance by Alan Guth and others. There have appeared a number of ideas in that field, for instance that of eternal / chaotic / open inflation by Andrei Linde.

All contradictions withdraws if take as a basis the law of conservation of Time Cycle of objects (universe in particular). In this case the universe can enlarges, in the same way can compresses. These phenomenas can be as global , in the same way can be as local. It is possible to present universe as a complex system with automatic regulation.

## 1. What is the current accepted value for the radius of the observable universe?

The current accepted value for the radius of the observable universe is approximately 93 billion light years. This distance is constantly changing as the universe continues to expand.

## 2. How is the radius of the observable universe measured?

The radius of the observable universe is measured using various methods such as the cosmic microwave background radiation, redshift of galaxies, and the use of standard candles such as Type Ia supernovae. These methods provide consistent estimates of the universe's size.

## 3. Can the radius of the observable universe be larger than the age of the universe?

No, the radius of the observable universe cannot be larger than the age of the universe. This is because the observable universe is limited by the speed of light and the age of the universe is the maximum amount of time that has passed since the Big Bang.

## 4. Has the radius of the observable universe always been the same?

No, the radius of the observable universe has not always been the same. It has been expanding since the Big Bang and will continue to do so in the future. The rate of expansion has also changed over time due to the influence of dark energy.

## 5. Is the observable universe the same as the entire universe?

No, the observable universe is not the same as the entire universe. The observable universe is the part of the universe that we can see and detect with our current technology. It is estimated to be only a small fraction of the entire universe, which may be infinite in size.

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