### Degrees of Freedom

The boundless dimensions of math and physics

# What Do You Mean, The Universe Is Flat?, Part 1

The universe is three-dimensional.
The universe is four-dimensional—three for space, one for time.
The universe has nine, or ten or eleven dimensions.
Matter curves spacetime.
The universe is flat.
The universe is infinite.
The universe is 84 billion light-years wide.
The universe is a bubble, or an onion.
Or a hall of mirrors, shaped like soccer ball.
Or a shape out of Dante’s Divine Comedy.

Statements like these appear quite frequently in popular science magazines–including Scientific American–and they seem to be in utter contradiction with one another. But all of them are true, or at least plausible. What gives?

The subtlety is that the word “universe” has different meanings in different contexts. In colloquial English, the word is often taken to mean “everything that exists.” So this intuitive notion of universe seems like a good place to start. If we follow this line of thought, the first thing we notice is that the present tense of the verb “to exist” implicitly assumes that we are referring to “everything that exists now.”

Leaving aside the issue of whether “now” can have a universal meaning–and the even subtler ontological question of what it means to exist–it makes sense to think of the totality of space and all of its contents at the present time, and to imagine this totality as a contiguous entity.

Space or spacetime?

If we take this route, we may first notice that space appears to us to be three-dimensional. Thus, we could make the assumption that we can locate anything in the universe using three Cartesian coordinates: at this frozen moment in time that we call the present, every object occupies a certain x, y and z in our three-dimensional continuum.

So here is one natural notion of the universe: all of three-dimensional space at the present time. Call it the nowverse.

But what about all those other dimensions?

Fanciful theoretical constructs such as string theory postulate that, in fact, there is more to space than we can see, but for now those theories have no experimental evidence to support them. So, for the time being we may as well just focus on our familiar three dimensions.

In this schematic of spacetime, the disk at the top represents space at the present time; the ones below represent space at earlier times

Time, on the other hand, is indeed an additional dimension, and together with space it forms a larger, four-dimensional entity called spacetime. It is natural to think of the nowverse as a 3-D slice in this 4-D space, just like horizontal planes are 2-D slices in our 3-D world. Because most people (including yours truly) have a hard time visualizing 4-D objects, a common way of thinking of spacetime is to pretend that space had only two dimensions. Spacetime, then, would have a more manageable total of three. In this way of looking at things, the nowverse is one of many parallel planes, each of which represent the universe at a particular time of its history.

Thus, the seeming inconsistency of

The universe is three-dimensional.
The universe is four-dimensional—three for space, one for time.
The universe has nine, or ten or eleven dimensions.

is just a matter of clarifying language. For all we know, space is 3-D, and spacetime is 4-D; but if string theory is true, then space turns out to be 9-D, and spacetime 10-D.

Incidentally, when cosmologists talk about the expansion of the universe, they mean that space has been expanding, not spacetime.

Flat or Curved?

A plane and the surface of a sphere are the prototype for flat and curved space

In the last decade—you may have read this news countless times—cosmologists have found what they say is rather convincing evidence that the universe (meaning 3-D space) is flat, or at least very close to being flat.

The exact meaning of flat, versus curved, space deserves a post of its own, and that is what Part II of this series will be about [update July 31: read What Do You Mean, The Universe is Flat? Part II: In Which We Actually Answer the Question]. For the time being, it is convenient to just visualize a plane as our archetype of flat object, and the surface of the Earth as our archetype of a curved one. Both are two-dimensional, but as I will describe in the next installment, flatness and curviness make sense in any number of dimensions.

What I do want to talk about here is what it is that is supposed to be flat.

When cosmologists say that the universe is flat they are referring to space—the nowverse and its parallel siblings of time past. Spacetime is not flat. It can’t be: Einstein’s general theory of relativity says that matter and energy curve spacetime, and there are enough matter and energy lying around to provide for curvature. Besides, if spacetime were flat I wouldn’t be sitting here because there would be no gravity to keep me on the chair. To put it succintly: space can be flat even if spacetime isn’t.

Moreover, when they talk about the flatness of space cosmologists are referring to the large-scale appearance of the universe. When you “zoom in” and look at something of less-than-cosmic scale, such as the solar system, space—not just spacetime—is definitely not flat. Remarkable fresh evidence for this fact was obtained recently by the longest-running experiment in NASA history, Gravity Probe B, which took a direct measurement of the curvature of space around Earth. (And the most extreme case of non-flatness of space is thought to occur inside the event horizon of a black hole, but that’s another story.)

On a cosmic scale, the curvature created in space by the countless stars, black holes, dust clouds, galaxies, and so on constitutes just a bunch of little bumps on a space that is, overall, boringly flat.

Matter curves spacetime. The universe is flat

is easily explained, too: spacetime is curved, and so is space; but on a large scale, space is overall flat.

Finite or Infinite?

If everything in the nowverse has an x, a y and a z, it would be natural to assume that we can push these coordinates to take any value, no matter how large. A spaceship flying off “along the x axis” could then go on forever. After all, what could stop her? Space would need to have some kind of boundary; most cosmologists don’t think it does.

The fact that you can go on forever however does not mean that space is infinite. Think of the two-dimensional sphere on which we live, the surface of the Earth. If you board an airplane and fly over the equator, you can just keep flying—you’ll never run into the “end of the Earth.” But after a while (assuming you have enough fuel) you would come back to the same place. Something similar could, in principle, happen in our universe: a spaceship that flew off in one direction could, after a long time, reappear from the opposite direction.

Or perhaps it wouldn’t. Cosmologists seem to believe that the universe goes on forever without coming back—and in particular, that space has infinite extension. But when pressed, most cosmologists would also admit that, in fact, they have no clue whether it’s finite or infinite.

In principle, the universe could be finite and without a boundary—just like the surface of the Earth, but in three dimensions. In fact, when Einstein formulated his cosmological vision, based on his theory of gravitation, he postulated that the universe was finite. Einstein’s Weltanschauung was rooted in his deep, almost mystical sense of aesthetics; the most symmetric, aesthetically perfect three-dimensional shape is that of a three-dimensional sphere. (Some have suggested that the way Dante describes the universe in his Divine Comedy has something to do with a 3-D sphere, too: I guess that will have to wait for a future post, too.)

In more recent times, some cosmologists have taken this possibility quite seriously, and have tried to check whether space might be a 3-D sphere, or perhaps a more complicated 3-D space that is essentially a sphere wrapped around itself [see “Is Space Finite?” by Glenn D. Starkman, Jean-Pierre Luminet and Jeffrey R. Weeks; Scientific American, April 1999]. In a universe that has one of these shapes, one could observe trippy hall-0f-mirror type of effects.

The reason why we don’t know if space is finite or infinite is that we seem to have no way of observing beyond a limited horizon. The universe is 13.7 billion years old, and because nothing can travel faster than the speed of light, we don’t have any information about events that happen beyond a certain distance. (For reasons that would be too complicated to go into here, that maximum distance is actually not 13.7 billion light years.)

The observed universe

So one thing we know is what we cannot know: the universe we can observe has finite extension. Cosmologists often refer to it as the observable universe.

How large is the observable universe? That is a surprisingly difficult question, which will be the subject of yet another future post.

For now, let’s just notice that the most distant galaxies whose light we have detected emitted that light about 13.2 billion years ago. Because the universe (meaning space) has been expanding ever since, those galaxies are now at a much greater distance—some 26 billion light-years away.

Even farther away than the farthest galaxies, the most distant object we have been able to observe, the plasma that existed before the age of recombination [see Under a Blood Red Sky], existed about 13.7 billion years ago, a puny 400 millennia after the big bang. Light coming from it has taken 13.7 billion light years to reach us. The matter we “see” in that plasma has also moved farther away: that matter is now an estimated 42 billion light years away. So that’s what cosmologists talk about when they say that the observable universe has a radius of 42 billion light years. (Of course, the answer had to be 42.)

The  bizarre fact about the observable universe, however, is that it is not part of the nowverse. Because light from distant galaxies took millions of years to reach us, what we see is in the past, not in the present, and the farther it is, the older it is. So if the observable universe is not part of the nowverse, how can we picture it? Where in spacetime should we place it?  [to be continued]

 This post is part of a series on cosmology. Here are the other posts:  What Do You Mean, the Universe Is Flat?, Part 2: In Which We Actually Answer the Question (“Flat” means “not curved,” but what does “curved” mean?) Being Mister Fantastic (On visualizing a finite speed of light) Under a Blood Red Sky (On the afterglow of the big bang, and why the sky used to glow red) Still to come: how do we know that the curvature of space is a fact of life; what would the world look like if space were very curved; what is the curvature (and the size) of the observable universe; and what the heck does the observable universe have to do with Dante.

Hubble Ultra Deep Field view courtesy of NASA. Sphere-and-plane image by Joe Doliner.

Many thanks to Scientific American cosmology guru George Musser.

About the Author: Davide Castelvecchi is a freelance science writer based in Rome and a contributing editor for Scientific American magazine. Follow on Twitter @dcastelvecchi.

The views expressed are those of the author and are not necessarily those of Scientific American.

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1. 1. jtdwyer 6:33 pm 07/26/2011

The article states:
“Incidentally, when cosmologists talk about the expansion of the universe, they mean that space has been expanding, not spacetime.”

I’m certainly not a cosmologist and am not an expert in general relativity, but I think you’ve missed something fundamental – that the dimensions of time and space are inseparable. Just like objects of mass locally curve their surrounding spacetime, as I understand the variable expansion of universal space must also vary the progression of time.

If I’m wrong, please explain more fully and/or provide supporting reference material so that I can better understand.

2. 2. pulpus 7:27 pm 07/26/2011

I suspect a small typo. Where you wrote
“For now, let’s just notice that the most distant galaxies whose light we have detected emitted that light about 13.2 years ago.”
maybe you meant:
“For now, let’s just notice that the most distant galaxies whose light we have detected emitted that light about 13.2 billion years ago.”

For the rest, thumbs up! I am waiting for the next part!

3. 3. elderlybloke 7:58 pm 07/26/2011

jtdwyer ,
It is just space which is expanding due to the vacuum energy of space called dark energy .
Dark energy accounts of 73% of all matter in the Universe.(Only known about since 1998)

Strange place the universe.

4. 4. @dcastelvecchi 10:32 pm 07/26/2011

Hi jtdwyer,

To say that something is expanding means that you are following the changes of an object through time. Spacetime is a single entity that encompasses both space and time, so spacetime itself does not change (otherwise time would be two-dimensional).

Now pretend for this discussion that spacetime had three dimensions, and choose a reference frame in spacetime. The reference frame assigns an x, a y and a t to every point in spacetime. The totality of points where t has a given value is by definition “space at that time”: for example, for t=13.7 billion years it is “space at time 13.7,” i.e., the present universe.

Space and time are inseparable, as you say, in the sense that if you change reference frame, you don’t necessarily get the same subdivision into constant-time surfaces and thus the same notion of “space.”

But once you’ve fixed a universal convention for time, you can “separate” space and time–as long as you keep in mind that your subdivision is conventional, i.e., does not have physical meaning.

In our universe there is a natural choice of such a convention, and that’s the frame of reference with respect to which the cosmic microwave background is approximately the same in all directions. Incidentally, Earth, due to its orbital motion, to the motion of the sun in the Milky Way, and to the peculiar velocity of the Milky Way itself, is not at rest in this frame of reference. It is moving in it at about 600 kilometers per second.

As a reference I could point you to Robert Wald’s textbook, or to Barret O’Neill’s, but either one requires a considerable investiment of time.

5. 5. @dcastelvecchi 10:34 pm 07/26/2011

elderlybloke,

Space is expanding in part because of dark energy but also because of the initial impulse it received in the big bang.

6. 6. jtdwyer 11:57 pm 07/26/2011

elderlybloke,
Yep – I heard it’s probably stranger than we can know…

The proposed acceleration of universal expansion is explained in an extensive overview:
“The Accelerating Universe”,
http://arxiv.org/abs/1010.1162

If you get really interested you can read the two initial research papers reporting observations supporting an accelerating universe requiring some hypothesized dark energy:

“Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”,
http://arxiv.org/abs/astro-ph/9805201v1

“Cosmological Results from High-z Supernovae”,
http://arxiv.org/abs/astro-ph/0305008v1

As I understaand, the universe is thought to have been initially expanding with little or no help from any dark energy, but for the first 8 billion years or so expansion continuously decelerated. As I understand, only observations of type Ia supernovae around 1 to 5 billion years ago are interpreted by astronomers to indicate that expansion is currently accelerating. However, nearer, more recent supernovae cannot be calibrated to determine whether they directly indicate acceleration or not.

Universal expansion has occurred regardless of the existence of any hypothetical dark energy. I still question the correctness of the author’s statement (that universal expansion affects only spatial dimensions, not the progression of time) in the context of spacetime as described by general relativity.

7. 7. jtdwyer 12:28 am 07/27/2011

Hi @dcastelvecchi,

Thanks for responding. I’m not going to become a physicist, but I do try to understand the concepts of physics, at least in overview.

With some additional investigation I do see that expansion is commonly considered to affect spatial dimensions only. However, I thought I understood that general relativity was able to treat the speed of light as a universal constant only because the progression of time varied with the alteration of spatial dimensions. If the progression rate of time is treated as a universal constant in relation to spatial distances aren’t conflicts with a constant speed of light produced? This would seem to be a critical issue since the speed of light is used to determine distances…

I realize that this is a difficult subject and that I haven’t taken any prerequisite courses, but I do appreciate your help.

8. 8. @dcastelvecchi 11:01 am 07/27/2011

jtdwyer said: “the progression of time varied with the alteration of spatial dimensions.”

I think what you may be referring to is the fact that when you change from one system of coordinates to another (for example from that of the train station to that of the train) the time coordinate is affected, too. But if you fix a coordinate system, then you don’t have such problems: you can “synchronize clocks” and treat time as flowing at the same rate everywhere (i.e. for all observers who are at rest in the coordinate system).

By the way, I didn’t mean to scare people off with references to graduate-level textbooks: I am sure that more accessible introductions exist somewhere on the Web, I just haven’t done the research to be able to recommend some. If anyone has good links, please add them below.

Besides, to illustrate the point about choosing reference frames one doesn’t need general relativity, just the much simpler special relativity. In future posts I may add a “more mathy” section at the end for those who want more details.

9. 9. suitti 11:45 am 07/27/2011

One such fairly easy introduction to Relativity was written by Einstein. Really. Einstein wrote to be read, and was quite good at it. The text is downloadable for free from project Gutenberg:

http://www.gutenberg.org/ebooks/5001

http://librivox.org/relativity-by-albert-einstein/

There’s a little math, which you can ignore. I listened to it recently, and was able to picture the math. I’d had some prior introduction, and lots of math and science however. Most of the book is the thought experiments, which though weird, were pretty easy to follow.

10. 10. lazzy_8 12:12 pm 07/27/2011

The article states: “The matter we “see” in that plasma has also moved farther away: that matter is now an estimated 42 billion light years away. So that’s what cosmologists talk about when they say that the observable universe has a radius of 42 billion light years.”
How can it be that the plasma has moved further away than 13.7 billion light years? I thought that anything moving at the speed of light could have only traveled 13.7 billion light years away. Therefore that the radius of the universe would seem to be 13.7 billion light years.

11. 11. @dcastelvecchi 12:46 pm 07/27/2011

lazzy_8:

What relativity says is that nothing can go past you faster than the speed of light. But because space itself is expanding, anything that’s distant enough is receding from you faster than the speed of light.

12. 12. pedronay 2:03 pm 07/27/2011

What good think about space without reference to matter? Our idea of space in three dimensions comes from our measurements of the bodies and the separation between them, and to assimilate both the geometric theory either.

What good is thinking of time without reference to space? Our idea of ​​time, whether classical or Einsteinian, comes from the calculation of the distance between the bodies, ie the space. Even we have a chronological record mental space where our memories and locations.

We know that the latest theories of quantum space understand that particles appear and disappear from existence. We know that particles are energy, energy that makes up our material world. Therefore, away from the two short arguments presented in the two preceding paragraphs, if we understand the notion of time depends on the space and the notion of space depends on the material, ie, the energy, I think we need theory would rather it left on his assumption of power. A good example is the Electric Universe theory.

13. 13. jtdwyer 4:02 pm 07/27/2011

@dcastelvecchi wrote:
“…if you fix a coordinate system, then you don’t have such problems: you can “synchronize clocks” and treat time as flowing at the same rate everywhere (i.e. for all observers who are at rest in the coordinate system).”

Well, I don’t know, but I think that if you universally ‘fix a coordinate system’ you’ve disassociated your universe from the principals of relativity, upon which modern physical cosmology was founded.
As I understand, the majority of the universe is now unobservable (disregarding any dark matter): many of the observed most distant objects are no longer observable as they are presumed to be so distant that any of their less ancient light emissions can’t have reached us yet.
If the universe is assumed for a moment to represent an expanding spherical surface, the temporally observable portion of the universe can be envisioned as a cone, the surface of which becomes increasingly flattened with the expanding relative scale of the universe.
It seems to me that, while the average density of the currently observed universe can be characterized, the absolute average density of the temporally developing universe cannot be correctly characterized since the temporally observable proportion of the universe varies as expansion proceeds.
While space or spacetime continues to expand, the distribution of mass or matter is increasingly localized by the proximal effects of gravitation. As a result, at large scales matter appears to be increasingly contained within large scale structures, while space is increasingly represented by large scale voids.
I suggest, then, that the ‘flatness’ of the universe, determined by the ‘average’ density of matter has become increasingly indeterminable and meaningless at large scales. Personally, I think that cosmologists, perhaps once the smartest people in the room, have effectively painted themselves into an ever more tightly constrained corner, now self determined by their own system of fixed universal coordinates…

14. 14. @dcastelvecchi 8:22 pm 07/27/2011

jtdwyer:

It seems that you have philosophical aversion to coordinate systems. I can assure you however that there’s no harm in using them — as long as one knows how to switch from one system to another and stays aware of what is coordinate-dependent and what isn’t.

15. 15. jtdwyer 11:28 pm 07/27/2011

@dcastelvecchi:

Sorry for being obstinate, but I can’t conceptualize how the expansion of space could avoid effecting the progression rate of time. If for no other reason, increasing distances between objects of mass would ‘decompress’ intervening spacetime, altering the gravitational effects imparted within local spacetime. Since gravitation affects the progression rate of time and the expansion of space is universally effective, how could expansion not also (universally) effect the locally variable progression rate of time?

From this perspective, I think it’s incorrect to consider universal expansion in relation to a fixed rate of time progression. More directly, as expansion dispersed the universe it (as I understand) must have reduced mass-energy density, decelerating expansion. In this case the progression rate of time should have, in general, ‘universally’ diminished.

In the meantime, I’d think that the speed of light remained constant in relation to the expansion of the universe – physically imparted to the extension of its wavelength as it propagated through spacetime.

Obviously I don’t really know anything about it, but it’s certainly more convenient for cosmologists to simply consider universal expansion in the context of a fixed progression rate of time…

16. 16. @dcastelvecchi 11:38 pm 07/27/2011

jtdwyer:

If I am not mistaken, the progression of time — in the sense of proper time of an observer — is what it is. It doesn’t depend on coordinates or gravity or the expansion of the universe. When we observe time getting stretched one way or another it means that we are comparing our proper time with that of other observers that are not at rest with respect to us.

17. 17. jtdwyer 3:32 am 07/28/2011

I may be imagining that time and space are considered to have been produced by the big bang – initiation of our universe. I don’t think that any observers of the progression of time in the 1 billion year old universe, for example, could have been at rest in respect to us.

18. 18. GoodLibran 4:04 am 07/28/2011

Hi Davide,

If the universe is finite, then mathematically it is zero compared to the infinite (space). But the question whether space and universe are finite or infinite is itself absurd. Infinity is not a number, it is a describable but an undefinable concept. Beginning and end of both space and universe, begin and end with our observational limits.

Space and universe (everything tangible) are simply meant to complement each other. Space is a meaningless concept without something in it and universe can only exist in space.

19. 19. howardpelling 6:04 am 07/28/2011

“The bizarre fact about the observable universe, however, is that it is not part of the nowverse.”
The logical implication of this is that the “Nowverse” is infinitely small (or does not exist), as light takes a finite amount of time to travel, even between atoms.

20. 20. @dcastelvecchi 9:35 am 07/28/2011

howardpelling:

I’ll clarify in Part II what I meant by not being part of the nowverse. It does not necessarily imply having zero size; but curiously, the most direct answer to the question “what is the size of the nowverse?” happens to be “zero.” That’s because the nowverse part of what is called the lightcone of our past. Distances along the lightcone are zero.

21. 21. MargaretaStammler 6:25 pm 07/28/2011

I do really like this, that a human NOT is able to understand the so very mega huge complex composition of Universe / Nowerse – We as simpy as this at first have to accept that common and prooved valid data on this planet NOT is able to applicate on universe/nowerse.
I have alwasy strongly disliked Albert Einstein and as long humanity has his “blinkers” ref reality, human nature will not proceed in any directions.Thank you for this very good article

22. 22. verdai 7:41 pm 07/28/2011

—-heavens! never heard of anyone disliking Einstein.
pretty amusing.

In any case, we cannot consider space to be matter/mass. Nor time. Nor flat. Nor fast.

23. 23. jack.123 8:58 pm 07/28/2011

Let’s see if I got this right.!st space=time can travel faster than the speed of light.2nd time is the the motion of mass and or energy through space.Thus it is space-time that prevents anything from traveling faster than the speed of light.What we see as red shifting is in fact the drag that caused by space-time as photons pass through it.It is this drag that also cause’s time which is attached to space to slow down and the bow shock of space-time that cause’s mass to increase.This may be a simplistic way of looking at these things,but if anyone wishes to input something to this theory please do so.Now lets get back to space-time traveling faster than the speed of light where entangled photons are are concerned.Now photons can’t pass information faster than the speed of light,but wave function drop can.While observing one entangled photon it causes wave function drop in the other.And it is through this drop that that information can be passed.I have in the past spoke of a design that can see whether wave function is present or not without itself causing wave function drop to occur if it is there a 0 and not a 1 and doing this you can send a binary signal faster than light.

24. 24. elling 9:50 pm 07/28/2011

Just a simple question; Where is “here” within the observable ‘bubble’ with a radius of 13.7 gyr? It would seem that as far as the size of the ‘nowuniverse’ is concerned, that would be the center, which might seem a bit ancient religious doctrine, rather than science?
Might it be that we have no idea about the actual size, or what our position might be, nor the age? Just, where we were relative to other objects in the distant past?

25. 25. majic21 9:53 pm 07/28/2011

An inspiring and engaging post! Can’t wait for the follow up(s) in this series. I really enjoyed the reference to Douglas Adams’ Deep Thought computer in the end (the answer is indeed 42)…

26. 26. @dcastelvecchi 10:49 pm 07/28/2011

elling:

We are indeed at the center of the visible (to us) universe. This does not violate the so-called Copernican Principle, or principle of mediocrity. The visible universe for an observer located somewhere else is different than the one we see. Think about sitting in a room with no windows: what you see is your visible universe. That doesn’t mean that the room is THE universe.

27. 27. Bill Crofut 11:16 am 07/29/2011

Davide,

Re: “…most people (including yours truly) have a hard time visualizing 4-D objects…”

We would seem to be in good company:

“It is impossible to imagine a four-dimensional space.”
[Prof. Stephen Hawking. 1996. A Brief History of Time. New York: Bantam Books, p. 35]

Matter curves spacetime. The universe is flat

is easily explained, too: spacetime is curved, and so is space; but on a large scale, space is overall flat.”

The contradiction does not seem, to me, to have been explained (i.e., space is curved on a small scale, but flat on a large scale). What is the definition of space in this context? Further in the post it’s described as “the universe.”

28. 28. @dcastelvecchi 12:11 am 07/31/2011

Bill: There is anecdotal evidence that some mathematicians, after years of practice, are indeed able to visualize 4-D objects.

By space I mean the nowverse. It is flat overall, in the sense that if you could hold a region billions of light years wide in your hand–for simplicity, visualize that region as being a two dimensional surface–it would look perfectly flat to the naked eye. But if you “zoomed in” you’d see little bumps that you couldn’t see before. Those bumps are caused by local concentrations of matter (stuff like galaxies, stars, interstellar dust and, above all, dark matter).

29. 29. jtdwyer 9:48 pm 07/31/2011

The article states:
“Even farther away than the farthest galaxies, the most distant object we have been able to observe, the plasma that existed before the age of recombination [see Under a Blood Red Sky], existed about 13.7 billion years ago, a puny 400 millennia after the big bang. Light coming from it has taken 13.7 billion light years to reach us.”

– As I understand, the universe is currently estimated to be 13.7 billion years old (Gyo) – that is when it is thought that the big bang occurred. The initial release of light (initially infrared now redshifted to microwave) is thought to have occurred 380,000 years after the big bang, or about 13.3 billion years ago. Please see:
http://en.wikipedia.org/wiki/Big_bang

– Cosmologists may derive a size (42Gly) for some presumed diameter of the ‘observable universe’, but as I understand astronomers only claim to have observed stars and galaxies that are just slightly more than 13Glya. Please see: Bouens, et al, (2011), “A candidate redshift z ≈ 10 galaxy and rapid changes in that population at an age of 500 Myr”,
http://www.nature.com/nature/journal/v469/n7331/full/nature09717.html

I must object to the idea of an ‘observable universe’ that contains mostly objects that cannot be observed. At best I suggest that cosmologists should refer to their 43 billion light year diameter ‘imaginary view’ as the ‘extrapolated universe’ or the ‘extended universe’.

I suggest that we cannot definitively determine that the observed CMB was emitted by any material that has not since been observed as objects within the actually observed universe. Unless we can now observed all of the initially released light emissions, there must have been many emissions that we cannot observe. There certainly may be matter that we cannot observe, but I do not think we have enough information about it for cosmologists to make any determinations about it.

30. 30. jtdwyer 10:05 pm 07/31/2011

I may be misunderstanding something, but I think that astrophysicists make assessments about the flatness or curvature of the universe based on observations of objects derived from not recent and ancient light emissions. Mustn’t the shape of the universe be assessed at varying times, since the expanding universe develops temporally? For example, the observable area on the surface of an inflating balloon, observed from any point on the surface of the balloon, becomes larger and flatter as the surface expands. What ever the actual geometry of the expanding universe, its apparent flatness or curvature and, separately, might not its actual flatness or curvature may vary over time? If so, any average of flatness or curvature indicated by observations of objects representing different times in the expansion of the universe would be meaningless.

31. 31. jtdwyer 10:08 pm 07/31/2011

Correction: the first sentence above should read:
I may be misunderstanding something, but I think that astrophysicists make assessments about the flatness or curvature of the universe based on observations of objects derived from recent and ancient light emissions.

32. 32. jtdwyer 10:11 pm 07/31/2011

The first error was mine. In the correction the comment application omitted the word BOTH enclosed in brackets:
…derived from BOTH recent and ancient light emissions.

33. 33. @dcastelvecchi 10:43 pm 07/31/2011

jtdwyer: what you are saying makes sense, but I was saying something else. Imagine that you have a balloon with a texture that’s not completely smooth. After you’ve been inflating your balloon, its surface may look flat locally, but if you look close enough you could still see its bumpy texture.

34. 34. jtdwyer 3:59 am 08/1/2011

@dcastelvecchi: Thanks, but wouldn’t it be more accurate to say that as the largest observable scales the geometry of the universe flattens with expansion, whereas the texture or local curvature of spacetime increases with the continuing accretion of galaxies?

After all, if all of the universe’s matter was condensed during the big bang and is only reprocessed by stars to continuously produce heavier elements, and galaxies have continued to merge for the past some 12Gy, locally and regionally producing ever more massive large scale structures as well as increasingly larger voids?

I think that both effects are at work, with the materially localizing, proximally focused effects of gravitation produce increasing texture at local and regional scales (relative to the scale of the universe), whereas the expansion of space temporally increases the apparent geometric flatness of the observable universe.

Again, I’m not sure how astronomers are assessing the flatness of the universe, but I’m concerned that the may be considering the entire temporally diverse population of observed objects to indicate some overall ‘average’ flatness or curvature, ignoring temporal developments…

35. 35. @dcastelvecchi 9:20 am 08/1/2011

jtdwyer said: “wouldn’t it be more accurate to say that as the largest observable scales the geometry of the universe flattens with expansion, whereas the texture or local curvature of spacetime increases with the continuing accretion of galaxies?”

I would say that’s more detailed because it explains how the geometry space has been evolving. I was just giving a snapshot of the present time and not to overwhelm the reader with too much information

36. 36. Bill Crofut 10:14 am 08/1/2011

@dcastelvecchi,

Re: comment 28

Mathematical anecdotes are precisely that. Please provide a readily-available reference in which a 4-D visualization claim is made.

Visualizing a 2-dimensional surface is no problem; the typical tourist map is 2-dimensional. Since no one is able to hold a piece of the cosmos billions of light
years wide in the hand, how can any astronomer/cosmologist make any definitive statement regarding content, especially “dark matter?”

37. 37. Torbjörn Larsson, OM 12:54 pm 08/1/2011

One argument for an infinite universe is that it is the simplest model from current parameters.

Another is symmetry, if the universe is forward infinite (eternal). That is what the standard cosmology suggest so far. Eternal inflation, which may be the case, may even be backward eternal (Linde).

@ pedronay:

“We know that the latest theories of quantum space understand that particles appear and disappear from existence.”

Space or spacetime is not quantized (even though the later is emergent). In fact, tentative observations predicts that it is not. Supernova spectra energy and polarization may probe planck scales; they find them smooth.

“A good example is the Electric Universe theory.”

The “Electric Universe” is not a theory in the science sense. In effect it says that “whatever you see, is what I claim”. It is like “intelligent design” and such like.

Science theories states clearly what the result of observation should be.

@ GoodLibran:

“If the universe is finite, then mathematically it is zero compared to the infinite (space). But the question whether space and universe are finite or infinite is itself absurd.”

The first claim is incorrect, as there is no current understanding how to compare distributions of universes (which you take two samples out of), for instance as probabilistic distributions over multiverses. In that sense, what you say is currently the absurd claim.

The last is not absurd, see the beginning of my comment.

@ MargaretaStammler:

“I do really like this, that a human NOT is able to understand the so very mega huge complex composition of Universe / Nowerse”.

Actually the article explains that we _do_ understand this. If you are interested, Wikipedia articles may be a good start, or the other literature mentioned here.

@ jtdwyer:

“I’m not sure how astronomers are assessing the flatness of the universe, but I’m concerned that the may be considering the entire temporally diverse population of observed objects to indicate some overall ‘average’ flatness or curvature, ignoring temporal developments…”.

I am not sure of the details either, but I know they are very careful when teasing out this. You can measure cosmological redshift, which by way of the expansion is the unique foliation I thing you was looking for earlier. So it measures cosmological time, as we see it.

At the very least you can use standard cosmology to make self-consistent models based on that, so there is no difficulty of principle here.

38. 38. Torbjörn Larsson, OM 1:01 pm 08/1/2011

@ Bill Crofut:

“Mathematical anecdotes are precisely that. Please provide a readily-available reference in which a 4-D visualization claim is made.”

I would agree. There is also a tradition of telling such anecdote among mathematicians on courses (I heard similar), so it is suspect.

“Since no one is able to hold a piece of the cosmos billions of light years wide in the hand, how can any astronomer/cosmologist make any definitive statement regarding content, especially “dark matter?””

Ah, the infamous “where you there” claim.

Let me restate that to point out how absurd it is, not by analogy (that take you only so far) but equivalent simile:

“Since no one is able to hold his or hers grand grand grand grand grand parents in the hand, how can any person make any definitive statement regarding existence of his forefathers, especially their “cultural context”?”

39. 39. Torbjörn Larsson, OM 1:09 pm 08/1/2011

@ jtdwyer:

I should explain this better as it may seem to confusingly contradict the article and other comments:

“You can measure cosmological redshift, which by way of the expansion is the unique foliation I thing [sic!] you was looking for earlier.”

It didn’t _have to_ be like that. But it is; so we can use it.

40. 40. Bill Crofut 10:44 am 08/2/2011

Re: “Since no one is able to hold his or hers grand grand grand grand grand parents in the hand, how can any person make any definitive statement regarding existence of his forefathers, especially their “cultural context”?”

One is able to do that based on historically documented genealogy.

41. 41. GoodLibran 4:56 am 08/3/2011

@dcastelvecchi

Can you explain how space-time curvature explains gravity? And also see my post no 18.

42. 42. @dcastelvecchi 9:11 am 08/3/2011

GoodLibrarian: I certainly will do a post on curvature and gravity in the near future. Gravity involves the curvature not just of space but of spacetime.
Meanwhile, if you have the stamina to read a whole book on the topic, I recommend:
“Black Holes & Time Warps”
by Kip S. Thorne

43. 43. GoodLibran 2:40 pm 08/3/2011

@dcastelvecchi

Thanks, and it is GoodLibran.

44. 44. KaliMa 10:39 am 08/8/2011

My apologies if this question has been posed and answered already. I am not a science student, so my knowledge is a little more limited. How is it possible that the observable universe has a radius of 42 billion lightyears if what we see was emitted by the objects observed when they were only at a maximum of 13.7 billion lightyears away? If what we see is, indeed (and I don’t doubt they are), technically the past (of when it was 13.7 billion lightyears away from) then how can we say that the observable universe is really 42 billion lightyears when that light has yet to reach us? I hope I’m making myself clear… If you have any resources I can look at to help explain this better, too, I would be grateful.

45. 45. KaliMa 11:54 am 08/8/2011

Wait. Never mind. I think I figured it out.

46. 46. @dcastelvecchi 4:25 pm 08/9/2011

KaliMa:

My personal opinion is that it is actually a bit of astretch to say that the observable universe is 42 billion light years wide. What people mean by that is that the regions of space we observe now that are farthest in the past — the plasma before recombination — have now moved to a distance of 42 billion light years. It does not mean that we are observing any events that are happening at that distance.

Incidentally, at the time the plasma released the light that we now observe as microwaves the universe was much smaller. In particular, the distance from that plasma to the plasma that became us was in the order of millions, not billions, of light years.

So the figure 13.7 billion light years represents neither the distance from here to there now nor the distance from here to there then. It is really a distance in time, not in space.

47. 47. jtdwyer 10:15 pm 08/14/2011

@dcastelvecchi:
Exceedingingly well put!

However, to my simple mind ~13.2 billion light years also representes the actual distance traversed by the earliest EM emissions from the most distant luminous objects that have been actually observed.

As I understand, the ~13.3 billion year old infrared emissions produced by the reionization of matter now observed as the redshifted Cosmic Microwave Background. It seems to me that ~13.3Gly should also represent the distance traversed by the infrared light waves emitted by the generally isotropic distribution of highly energetic matter in the very early universe.

48. 48. @dcastelvecchi 12:19 am 08/17/2011

jtdwyer:

I am planning a whole post on this topic soon because I think it’s really interesting and a lot of people find it confusing — myself included!

49. 49. Brain1 7:24 pm 04/25/2012

THE ONLY THING THAT IS blatantly clear is all this will scrapped and filed away in the infinite pile of “We Now Know” proclamations.
If there is one thing absolute in the modern era..it is arrogance. Be sure about this…the next “We Now Know” is just around the corner yet nothing in history tells these guys that the last time they said it…it really meant,
” We now are fudging the data and calling it Knowing”.

There seems to be some grandiose back patting these guys Need to do to survive psychologically or get funding. Any outsider can see the whole thing is a fudged together mess yet they’re so certain that this time “They DO know” even though they were so certain every time before as well.

Just to illustrate..Mercury’s core–”we now know” and this sudden boldness from some about string theory when it is all but abandoned by the majority. You can thank fine tuning for the myopia there. I think the public deserves humble opinions and not conjecture masquerading as fact.

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