# how big is the universe?

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I know that the known universe is roughly 27 billion light years in diameter, but what about the unknown universe - that is, the universe even beyond what is visible?

I used to assume it just wasn't known how big it was until I came across a chart the other day depicting the rate of expansion of the early universe. It was like this:

Time: size:

10^-40s 1mm

10^-30s 100m

10^-20s Earth

10^-10s solar system

1s 10 Ly

Now I'm not sure how reliably we can extrapolate this chart to today's universe. The rate of expansion has been changing after all. From what I understand according to the inflationary theory, the universe started out by accelerating, then decelerated, and is now into an accelerating phase once again.

But given that physicists seem to have some kind of grasp on its rate of expansion and size at various points in its history, and that we know the age of the universe, can we estimate with any confidence its size today?

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• 2 weeks later...

Current interpretations of astronomical observations indicate that the age of the Universe is 13.73 (± 0.12) billion years, and that the diameter of the observable universe is at least 93 billion light years, or 8.80 × 1026 metres. According to general relativity, space can expand faster than the speed of light, although we can view only a small portion of the universe due to the limitation imposed by light speed. It is uncertain whether the size of the Universe is finite or infinite.

http://en.wikipedia.org/wiki/Universe

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Thanks Spyman.

This is the part that I'm a bit confused about:

It is uncertain whether the size of the Universe is finite or infinite.

I was under the impression that the universe could be thought of as the 3D surface of a 4D sphere and that all planets, stars, and galaxies were like objects on its surface. It expands like a balloon being filled with air.

But this means the universe is necessarily finite. Why would it be uncertain whether it is finite or infinite?

I started a thread similar to this here. Maybe you can comment on that one too if you have something to say.

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Nobody knows for sure whether the universe is infinite or not because nobody knows what is outside the range of our observations. What is certain is that it is really, really big in comparison to humans thus far in our history.

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The balloon analogy just doesn't work for me. My mind refuses to imagine the universe curving like the surface of a balloon. And IF 4D space can somehow be curved like a balloon, curved within what?

I much prefer to think of space as extending to infinity in every direction.

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Astronomers can put a lower limit on the size but, if the expansion rate doesn't redline, what lies beyond that has yet to arrive. If the rate becomes to great, it is likely no signal from that realm shall ever reach us, and we will never know.

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We may only be interested in the observable universe. Maybe the true boundaries of the universe are so far away that the light reflected off them hasn't reached Earth yet, and so we get an expanding area of the matter whose light reflected off it up to 13 billion years ago.

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I was under the impression that the universe could be thought of as the 3D surface of a 4D sphere and that all planets, stars, and galaxies were like objects on its surface. It expands like a balloon being filled with air.

But this means the universe is necessarily finite. Why would it be uncertain whether it is finite or infinite?

Because our best measurements has a 2% margin of error that could go either way.

The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were open, the brightest microwave background fluctuations (or "spots") would be about half a degree across. If the universe were flat, the spots would be about 1 degree across. While if the universe were closed, the brightest spots would be about 1.5 degrees across.

Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know that the universe is flat with only a 2% margin of error.

http://map.gsfc.nasa.gov/universe/uni_shape.html

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This is a hypothesis.

So, need to some attention.

Relations between radius of universe and dark energy density

fig11. Relations between radius of universe and dark energy density

* mass density of ordinary matter = 1 proton/5m3

* Proton mass= 1.67264 X 10-27kg

* G =6.6726 X 10-11 m3/s2kg

* 1J = 6.242 x 1018 eV

* $n_-=n_+=n, m_-=(23.3/4.6)m_+=(5.06522)m_p$

* $\bar r_{ - + } = \frac{R}{{3.27273}}$

* If $\bar r_{ - + } = \frac{R}{{2.17879}}$ $(U_T \approx 0)$, dark energy density has a 1/3 smaller than $\bar r_{ - + } = \frac{R}{{3.27273}}$.

In a WMAP, observed value $\Lambda = 2.14( \pm 0.13 )\times 10^{ -3} eV$

Dark energy density :

$\rho _{de} = 2.09 \times 10^{ - 47} [_{ - 0.465}^{ + 0.557} ]GeV^4$

Ridius of the Universe :

$R_{UNI} = 96.76[_{ - 11.44}^{ + 12.13} ]Gly = 85.32 \sim 108.89Gly$

( If $\bar r_{ - + } = \frac{R}{{2.17879}}$,

$R_{UNI} = 118.8[_{ - 14.0}^{ + 14.9} ]Gly = 104.8 \sim 133.7 Gly$)

From Neil J. Cornish,

the universe' radius is at least 24Gpc(78Gly).

(2003, Neil J. Cornish, "Constraining the Topology of the Universe", http://arxiv.org/abs/astro-ph/0310233v1 )

[Proof]

In negative mass hypothesis, dark energy is corresponding to that positive potential term in total potential energy.

*Potential energy between positive mass and positive mass has - value:$U = \frac{{ - G(m_ +) (m_ +) }}{r} = 1U_ -$

*Potential energy between negative mass and positive mass has + value:$U = \frac{{ - G( - m_ - )(m_ +) }}{r} = 1U_ +$

*Potential energy between negative mass and negative mass has - value:$U = \frac{{ - G( - m_ - )( - m_ - )}}{r} = 1U_ -$

When the number of negative mass is n_- , and the number of positive mass is n_+ , total potential energy is given as follows.

$U_T = \sum\limits_{i,j}^{i = n_ - ,j = n_ + } {(\frac{{Gm_{ - i} m_{ + j} }}{{r_{ - + ij} }})}$

$+\sum\limits_{i,j,i > j}^{i,j = n_ - } {(\frac{{ - Gm_{ - i} m_{ - j} }}{{r_{ - - ij} }})} + \sum\limits_{i,j,i > j}^{i,j = n_ + } {(\frac{{ - Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})}---(78)$

$U_T = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }})$

$+ (\frac{{n_ - (n_ - - 1)}}{2}(\frac{{ - Gm_ - m_ - }}{{\bar r_{ - - } }}) + \frac{{n_ + (n_ + - 1)}}{2}(\frac{{ - Gm_ + m_ + }}{{\bar r_{ + + } }})) ---(79)$

In equation (79)

$E_{de}=U_{de} = (n_ - \times n_ + )(\frac{{Gm_ - m_ + }}{{\bar r_{ - + } }})$

If radius of the universe is 60Gyr, ordinary matter density is about proton 1ea/5m3. So, m+ = mp,

$m_ - = km_ + \simeq (\frac{{23.3}}{{4.6}})m_ + = (5.06522)m_p$

(because that dark matter has about (23.3/4.6) times ordinary matter in WMAP)

From equation (95)

$\bar r_{ - +} =(60Gyr/3.27273)= 1.73447 X 10^{26}m$

From analysis of V-5,

If $U_T \ge 0$, $n_ - \approx n_ +$, Therefore, Define, $n_ - = n_ + = n$

$V = \frac{{4\pi R^3 }}{3} = \frac{{4\pi \times (5.67648 \times 10^{26} )^3 }}{3} = 7.66171 \times 10^{80} m^3$

$n = \frac{{\rho V}}{{m_p }} = \frac{{(1m_p /5m^3 )V}}{{m_p }} = 1.53234 \times 10^{80}$

( 1080 is about total proton number of our universe).

$U_{de} = (kn^2 )(\frac{{Gm_p^2 }}{{\bar r_{ - + } }})$

$U_{de} = (5.06522)n^2 \frac{{(6.6726 \times 10^{ - 11} )(2.79772 \times 10^{ - 54} )}}{{1.73447 \times 10^{26} }}J$

$U_{de} = (n^2 ) \times 5.45168 \times 10^{ - 90} J = 1.28009 \times 10^{71} J$

1J = 1kg(m/s)2 = 6.242 X 1018 eV

$U_{de} = 7.99031 \times 10^{89} eV$

$\rho _{de} = \frac{{U_{de} }}{V} = \frac{{7.99031 \times 10^{89} eV}}{{7.66171 \times 10^{80} m^3 }} = \frac{{1.04289 \times 10^{ - 6} GeV}}{{cm^3 }}$

Planck Unit transformation(1cm =0.5063 x 1014GeV-1 )

$\rho _{de} = \frac{{1.04289 \times 10^{ - 6} GeV}}{{1.29784 \times 10^{41} GeV^{ - 3} }} = 0.80355 \times 10^{ - 47} GeV^4$

$\rho _{de} = 0.80355 \times 10^{ - 47} GeV^4$

Observation value is $\rho _{obs} \approx 10^{ - 47} GeV^4$

If R=90Gyr, $\rho _{de} = 1.808 \times 10^{ - 47} GeV^4$(refer to fig11).

$\rho _{de} \approx \rho _{obs}$

[Proof end]

In Quantum Field Theory, the energy density of the vacuum is estimated as 1070GeV4, which is about 10117 orders of magnitude large than the observation value 10-47GeV4.

In a WMAP, observed value $\Lambda = 2.14( \pm 0.13) \times 10^{ -3} eV$

Dark energy density :

$\rho _{de} = 2.09 \times 10^{ - 47} [_{ - 0.465}^{ + 0.557} ]GeV^4$

Ridius of the Universe :

$R_{UNI} = 96.76[_{ - 11.44}^{ + 12.13} ]Gly = 85.32 \sim 108.89 Gly(billion-light-years)$

=========

Hypothesis of Dark Matter and Dark Energy with Negative Mass :

http://vixra.org/abs/0907.0015

Edited by icarus2
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Because our best measurements has a 2% margin of error that could go either way.

See, the problem I have with an infinite space is that it conflicts with my understanding of the Big Bang Theory. According to what I understand, the Big Bang began as a singularity (or something close to one) and this included space itself - that is to say, space itself began to expand with everything else. To my mind, the only model that fits this is the one of a 4D sphere where our 3D universe is its surface.

If the universe is flat or open, that means either space has expanded to infinity already (which is untenable) or there is some kind of limit to space - a "wall" so to speak - that is a finite distance away and can supposedly be encountered if one traveled far enough (which seems absurd to me).

An alternative is that space is infinite to begin with and the Big Bang occured at some local region in space. Space could still be said to be expanding according to this model, but not all of it starting from a singularity. The problem with this is that, from what I understand, the contents of the early universe (particles, gas, photons, etc.) are said to have filled all space and so they can't be limited to a local region.

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See, the problem I have with an infinite space is that it conflicts with my understanding of the Big Bang Theory. According to what I understand, the Big Bang began as a singularity (or something close to one) and this included space itself - that is to say, space itself began to expand with everything else. To my mind, the only model that fits this is the one of a 4D sphere where our 3D universe is its surface.

If the universe is flat or open, that means either space has expanded to infinity already (which is untenable) or there is some kind of limit to space - a "wall" so to speak - that is a finite distance away and can supposedly be encountered if one traveled far enough (which seems absurd to me).

An alternative is that space is infinite to begin with and the Big Bang occured at some local region in space. Space could still be said to be expanding according to this model, but not all of it starting from a singularity. The problem with this is that, from what I understand, the contents of the early universe (particles, gas, photons, etc.) are said to have filled all space and so they can't be limited to a local region.

If space is infinite, then it has always been infinite. Why would that imply that the Big Bang took place at some localized region? If anything, an infinite universe makes that especially nonsensical. The Big Bang took place everywhere. Just remember that infinity /= infinity.

Picture an infinite space, filled with particles spaced an average of 1 unit apart. Now expand the space itself, such that particles are an average of 2 units apart. See? Now collapse it, such that particles are infinitessimal distances apart. No problem. Infinite in all cases, but not the "same infinite."

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Sisyphus writes:

If space is infinite, then it has always been infinite. Why would that imply that the Big Bang took place at some localized region? If anything, an infinite universe makes that especially nonsensical. The Big Bang took place everywhere. Just remember that infinity /= infinity.

Why does a 'localized' BB seem nonsensical to you? Perhaps I am not understanding you. Define what you mean by 'everywhere'. If you mean that the process we are observing currently in OUR area of infinity is currently, and/or has in the past occurred isotropically throughout infinity, then would we not see 'other' CMBR red shifted to the extreme, along with the CMBR we are observing now?

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I'm not sure how to answer because I don't know what you're picturing. By everywhere I mean that the Big Bang was not an event that had a particular location in space, but that it was the beginning of the expansion of space, which is quite possibly infinite and certainly doesn't have a "center." I don't know what you mean when you say "other CMBR."

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Sisyphus writes:

I'm not sure how to answer because I don't know what you're picturing. By everywhere I mean that the Big Bang was not an event that had a particular location in space, but that it was the beginning of the expansion of space, which is quite possibly infinite and certainly doesn't have a "center." I don't know what you mean when you say "other CMBR."

______________I would be pleased to describe the ( theorized ) infinite universe, and our visible/local universe's relationship to it as I do have a clear 'picture' ( based on ... and not contradicted by ... known physics, Einstein's Uniformity of Space, etc ) but I am not certain this is the proper place to do this.

Perhaps "The assumption of bounded/unbounded space" might be more appropriate?

But if the OP would not object ... ?

Edited by pywakit
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If you're referring to your own personal ideas in contradiction with mainstream physics, then no, don't bring that into this thread.

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If you're referring to your own personal model, then no, don't bring that into this thread.

I wasn't. That is a seperate issue. I did however provide a general description of infinite space as an addendum following my model, so if you care to review that, you should find the answer to your questions posed above ... including the 'other' CMBR.

I should point out that we still do not know that 'space expands' at all. We only know that the galaxies receding from us are doing so at a rate proportional to distance, and that they exhibit little motion relative to CMBR.

Expanding space is one possible mechanism for these observations.

Merged post follows:

Consecutive posts merged
If you're referring to your own personal ideas in contradiction with mainstream physics, then no, don't bring that into this thread.

Yikes! Lol. I was unaware that ANY of my hypotheses, or theories 'contradicted' mainstream physics. Please feel free to elucidate on the appropriate thread ...

Anyway ... physics is physics. I don't think there is such a thing as non-mainstream physics, is there?

Surely you are not suggesting that ST, or the Expansion of Space is 'mainstream' physics? Mainstream hypothesis, or theory ... most certainly. But 'physics' have proven neither. ( to the best of my knowledge )

But I won't argue with you on this thread. My apology to the OP.

Edited by pywakit
Consecutive posts merged.
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There is a good presentation you can watch on Youtube from Allan Guth himself, at

In part four (Inflationary Cosmology Guth FOUR), someone of the assistance asks if the inflationary theory puts a center for the BB, and Guth's answer is positive.

PS. Pywakit will enjoy, especially part THREE, I am sure.

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There is a good presentation you can watch on Youtube from Allan Guth himself, at

In part four (Inflationary Cosmology Guth FOUR), someone of the assistance asks if the inflationary theory puts a center for the BB, and Guth's answer is positive.

PS. Pywakit will enjoy, especially part THREE, I am sure.

Michel thank you. The following is an excerpt from wiki:

Alan Guth believes that the size of the entire universe is at least 10^23 times bigger than the size of the observable universe. The universe also exists among countless other universes with various different laws of physics. A fractal pattern exists in the multiverse system, which involves universes inside vacuums that are inside other universes. Each pocket universe created by inflation will appear flat to the observers within it. Meanwhile, new universes will fill in the gaps created by older ones, similar to Hoyle’s discredited steady-state theory. The big bang of the universe is actually similar to cell division in biology, since new universes are continuously formed. However, inflation always wipes out the circumstances of the beginning of the particular universe.

Alan Guth's main beliefs about the universe are that it definitely has a beginning and that it is just one of many universes that came into existence. Inflation never ends, but keeps expanding at an exponential rate, meaning that it doubles in very short increments much less than one second. Universes keep being created all the time as bubbles within the inflation process. The entire cosmos was created by quantum fluctuations from nothingness. While the concept of a universe being created from nothing sounds improbable, it is perfectly consistent with the laws of conservation of energy because its total energy value is zero.

One theory that Guth is particularly fond of is string theory, which says that the building blocks of the universe are superstrings that are much smaller than elementary particles. According to the latest versions of this theory, there are about 10^500 possible vacuums in existence. The main reason why Guth supports string theory is that he feels that it is the only one that provides a working idea of quantum gravity, a concept that physicists have long been searching for.

There have been more than fifty additional inflation theories proposed since Guth's original model. Now that the Planck spacecraft was finally launched in 2009, it should provide data to help choose between the various theories of the details of inflation. The theory of inflation that wins out will certainly differ from Guth's original model, which he acknowledged was incomplete because of its inability to solve the "graceful exit" problem. But Guth will always be remembered as the person who revealed inflationary theory to the scientific community.

According to Guth’s theory of cosmic inflation, the universe originated from a false vacuum filled with high energy.

Really Michel, about the only thing Dr. Guth and I somewhat agree on is this last statement. And even this is suspect as there is some confusion over the definition of THE universe, and whether or not that 'false vacuum' existed eternally before our visible/local universe came along. Anyway, I had already sent him a copy of my model on 12/18/09 ... I doubt very much he found it amusing ... assuming he even read it.

However, when I have a spare moment I will review the youtube material.

Edited by pywakit
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See, the problem I have with an infinite space is that it conflicts with my understanding of the Big Bang Theory. According to what I understand, the Big Bang began as a singularity (or something close to one) and this included space itself - that is to say, space itself began to expand with everything else. To my mind, the only model that fits this is the one of a 4D sphere where our 3D universe is its surface.

If the universe is flat or open, that means either space has expanded to infinity already (which is untenable) or there is some kind of limit to space - a "wall" so to speak - that is a finite distance away and can supposedly be encountered if one traveled far enough (which seems absurd to me).

An alternative is that space is infinite to begin with and the Big Bang occured at some local region in space. Space could still be said to be expanding according to this model, but not all of it starting from a singularity. The problem with this is that, from what I understand, the contents of the early universe (particles, gas, photons, etc.) are said to have filled all space and so they can't be limited to a local region.

I think the general consensus among the science community is that there was no singularity in the beginning of Big Bang, instead the singularity is thought of as mathematical construct that indicates the break down of General Relativity when the scales becomes small enough.

If we remove the singularity from the Big Bang, we can conclude that universe was smaller back then and are bigger right now, and that doesn't exclude the possibility that space has been infinite all the time, and our visible part of it was much much smaller before all distances expanded to the scale we have now.

I think the trick is not to think about space as confined inside something or with strange boundaries like a wall somewhere out there. If you imagine a ruler and then have the distances expand between the markings on it, it really doesn't make any difference if the ruler continues on in infinity in both directions from our view point or not, the markings does still distance themself from each other.

The model of a 4D-sphere with expanding radius might be very attractive for a human mind, like yours or mine, but scientists always seeks ways to confirm their models with real measurements and so far all three models are valid from the precision of our observations.

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I think the general consensus among the science community is that there was no singularity in the beginning of Big Bang, instead the singularity is thought of as mathematical construct that indicates the break down of General Relativity when the scales becomes small enough.

If we remove the singularity from the Big Bang, we can conclude that universe was smaller back then and are bigger right now, and that doesn't exclude the possibility that space has been infinite all the time, and our visible part of it was much much smaller before all distances expanded to the scale we have now.

I think the trick is not to think about space as confined inside something or with strange boundaries like a wall somewhere out there. If you imagine a ruler and then have the distances expand between the markings on it, it really doesn't make any difference if the ruler continues on in infinity in both directions from our view point or not, the markings does still distance themself from each other.

Is this more or less what Sisyphus was saying? If it is, then it follows that the amount of matter and energy in the universe is infinite. Is this possible? If it's not infinite, then all matter and energy must be localized around a central point. It doesn't have to be condensed around that point, but if one were to travel far enough, one would eventually enter a region of space where no matter or energy existed (except for the person himself, of course). The universe would essentially have a center. I'm told that no such center exists, and so I must conclude that the amount of matter and energy, in this case, would be infinite. Is this tenable?

The model of a 4D-sphere with expanding radius might be very attractive for a human mind' date=' like yours or mine, but scientists always seeks ways to confirm their models with real measurements and so far all three models are valid from the precision of our observations.[/quote']

With a margin of error of 2%, a spherical universe would have to be pretty darn big - several times that of the visible universe. This makes me wonder how fast it was, and still is, expanding. This is why I posted those figures in my OP. They seem to suggest that scientists have some kind of grasp on how fast this expansion was going in the early universe, and I wonder if they fit with the notion of the universe being several times (hundreds?) bigger than the visible universe today.

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Is this more or less what Sisyphus was saying? If it is, then it follows that the amount of matter and energy in the universe is infinite. Is this possible? If it's not infinite, then all matter and energy must be localized around a central point. It doesn't have to be condensed around that point, but if one were to travel far enough, one would eventually enter a region of space where no matter or energy existed (except for the person himself, of course). The universe would essentially have a center. I'm told that no such center exists, and so I must conclude that the amount of matter and energy, in this case, would be infinite. Is this tenable?

That is what I was saying, yes. Anyway, it definitely doesn't have a center. The way expansion behaves isn't consistent with expanding away from some central point, like a conventional explosion. That doesn't mean it must be infinite, though. A relatively simple alternative is that it folds back on itself. i.e., that a long enough straight line just points back at itself. Think of it like a computer game where going off one end of the map puts you on the opposite side, but 3D. So the volume is finite, but it has no center and no edges.

With a margin of error of 2%, a spherical universe would have to be pretty darn big - several times that of the visible universe. This makes me wonder how fast it was, and still is, expanding. This is why I posted those figures in my OP. They seem to suggest that scientists have some kind of grasp on how fast this expansion was going in the early universe, and I wonder if they fit with the notion of the universe being several times (hundreds?) bigger than the visible universe today.

I forget where I saw it, but I remember some physicist claiming that if the universe is finite, then the ratio of universe to observable universe would have to be at least that of the Earth to a 1 inch sphere. I have no idea if that's a consensus or current view.

Edited by Sisyphus
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That is what I was saying, yes. Anyway, it definitely doesn't have a center. The way expansion behaves isn't consistent with expanding away from some central point, like a conventional explosion. That doesn't mean it must be infinite, though. A relatively simple alternative is that it folds back on itself. i.e., that a long enough straight line just points back at itself. Think of it like a computer game where going off one end of the map puts you on the opposite side, but 3D. So the volume is finite, but it has no center and no edges.

Hmm... I have difficulty dissociating this scenario with the model of a 4D sphere on which our 3D universe is its surface. I guess I could chalk the 4D sphere up to a useful conceptual tool only and that the real nature of space - that is, how it wraps around like you say - to something beyond my ability to comprehend.

But is there anything wrong with imagining an infinite amount of matter and energy filling the universe?

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"How big is the Universe?"

It's a good question, and one that I too have thought long and hard about

Recently, a solution dawned on me.., and I realized that a better question to ask is "How big is your appetite for Donuts?"

yes, I now believe that the size of the Universe is mass dependent!

(observers mass that is)

and that the size of the Universe can be written as...

r = (2Gm/H^2)^(1/3)

..which incidentally turns out, that observations match the mass of the average chubby Astronomer

Now we can feel better about that extra Donut...

Steven

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How big is the universe? Only God knows that one

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How big is the universe? Only God knows that one

Well, apparently not, seeing as the people in this forum are debating it. Regardless, whether god knows that or doesn't know that, he (or she) cannot participate in this forum debate, and is therefore irrelevant for the purposes of this thread.

~moo

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