# Requesting help on diagramming the universe

1. May 6, 2006

### Hulse

Problem:

I'm trying to do a diagram of the observable universe, and I got bogged down. I drew a circle representing the outer limit, the "surface of last scattering," 78 billion light years in diameter. In the center I put a tiny dot to represent us and the Local Group of galaxies. At two locations on the radius I put dots representing two known galactic clusters together with their "distances now" worked out by using Ned Wright's cosmology calculator. Then I drew two tangent circles, diameters equal to the original circle and labeled each perimeter "surface of last scattering." So the centers of all three circles formed a straight line of diameters. I reasoned that if one could jump in imagination to a tangent point, one would see exactly the same sort of sky one sees now from earth. Further, I reasoned that if the larger universe were closed, one could keep on drawing these tangent circles till they came round in a "band of tangent circles" to meet the original circle. But now I'm get the feeling I did something wrong, but I don't know what.

Can somebody who knows analyze my work, tell me if I made mistakes, show me how I should "diagram the universe," or if it's not diagrammable, tell me why it's not.

2. May 6, 2006

### hellfire

The radius of the observable universe is about 46 billion lightyears on the current spatial hypersurface. Besides of this it seams to me that your procedure is correct, because you are considerig a surface of constant time (a spatial hypersurface) and you can simply add the different circles. Actually, this procedure searching for patterns in the CMB was used to constraint the size of the universe. You may find this interesting.

3. May 7, 2006

### Hulse

Thanks Hellfire,

The distance 46 billion lightyears is a radius. So the diameter of the observable universe is 92 billion lightyears on the hypersurface of constant time. The number I used, 78 billion, is 14 billion lightyears smaller. I got that number from a news source, a cosmologist in the news who figured out the angular diameter from the CBM and inferred that smaller 78 billion number.

So my new question is how do we know the observable universe is 92 billion lightyears in diameter?

4. May 7, 2006

### hellfire

This is the current position on a hypersurface of constant time (this means you would measure this distance if you could use a material "cosmological" ruler) of a hypothetical massles particle sent from our comoving position at t = 0. It is more than 13.7 billion lightyears because space has expanded between us and this hypothetical particle. The actual value can be calculated making use of the first Friedmann equation. If you are interested in knowing the size of the observable universe for different cosmological models, you can visit this cosmological calculator. If you are interested in the technical details to derive this distance please let me know before what yor background knowledge is (it will be some work to write the steps in LaTeX).

Last edited: May 7, 2006
5. May 8, 2006

### ptalar

How can the radius of the Universe be 46 billion light years if the age of the Universe is purported to be 15 billion years. Wouldn't the radius be around 15 billion light years? What am I missing?

Phil

6. May 8, 2006

### Hulse

Hellfire wrote: "If you are interested in knowing the size of the observable universe for different cosmological models, you can visit this cosmological calculator. If you are interested in the technical details to derive this distance please let me know before what yor background knowledge is (it will be some work to write the steps in LaTeX)." (Sorry I haven't figured out how to use the quote function yet.)

Holy halucination, batdude! That's some awesome calculator! I respect it, but I can't use it. Neither would I be able, I regret, to follow your tech details. My profession is a science writer, and mostly medical science at that, though my first love is astronomy/cosmology. My job involves finding the most "reader friendly" scientist to quote.

That said, I would be most interested in reading your answer to Phil's question. That, so I can burgle it in explaining this common misperception to my own readers.

And thank you, Phil, for a clear, well-asked question.

7. May 8, 2006

### Garth

Two things.

First. You cannot see the whole universe, the finite age of the universe and the finite speed of light mean that there is a limit to how far you can see. Any further beyond this limit and it would take light longer to reach us than the entire age of the universe.

Second. The universe, that is space, is expanding, in GR expanding space carries galaxies and photons along with it. This means the actual distance we can see, the 'Radius of the observable universe" in hellfire's calculator link, expressed in light years, is greater than the universe's age in years and increases as the universe evolves.

The actual distance we can see, the radius of the observable unverse, is dependent on how the universe has expanded in the past and that varies with the amount of matter and energy in it. This is why you need a 'calculator', it is not trivial.

I hope this helps.

Garth

8. May 8, 2006

### pervect

Staff Emeritus
As others have remarked, to get a consistent set of numbers, you should determine the "diameter of the universe" using the same calculator that you use for your other calculations. This should be represented by plugging z=infninty into the calculator, though you might settle for the diagram of the visible universe instead, z=1100. (There is not that much difference).

All of the various calculators (Hellfire's and Ned Wright's) should wind up with the same answers for the same inputs. If they don't, complain on the forums, we can try and sort it out.

The problem of drawing a diagram of the universe is much like the problem of drawing a map of the world. Different diagrams (maps) will be good for different things. On the map of the world, the straightfowards mercator projections are commonly used, are good for navigation, but distort the shape and relative size of the contients.

In cosmology, there are similar problems, which arise for similar reasons - the geometry of the universe is not Euclidean, while the geometry of the maps drawn on a flat piece of paper is.

I think I would go with a set of three diagrams to try and give a good overview of the universe. I would plot the universe not only in space, but in time, contracting the 3 dimensions of space into one dimension on the graph.

diagram 1 would be a rectangluar graph, showing galaxies staying at a constant cosmological coordinate vs cosmological time. Lines of constant cosmological coordiantes would be vertical. Something like

http://www.astro.ucla.edu/~wright/cosmo220.gif

(The local lightcones would have to be explained, or more easily, just omitted).

It would be emphasized that the red lines in all diagrams were the light cone of our past.

diagram 2 would introduce conformal time, a rescaling of time so that light appears to travel at a constant velocity

http://www.astro.ucla.edu/~wright/cosmo230.gif

diagram 3 would show how galaxies, following constant cosmological coordinates, actually get further apart, by having the lines of constant cosmological coordinates slat so as to preserve co-moving distance. Something like

http://www.astro.ucla.edu/~wright/omega0.gif

These diagrams could then be used to explain why the universe is wider than it is old.

I would probably "shade out" the region for z>1100, explaining it is not visible with light. I think I would stop the conformal time diagram at z=1100, rather than get into the horizon problem and inflation, but I would add a shadded region for z>1100 and z<infinity to the other two diagrams.

Last edited: May 8, 2006
9. May 9, 2006

### Hulse

Re cosmological calculators: The reason why I was more intimidated by Hellfire's calculator than by Ned Wrights was that he actually e-mailed me the input numbers to plug in. I couldn't have come up with them on my own.

So there's not much difference between z=infinity and z=1100. Is this due to the asymtote on the on the redshift-versus-distance graph? Or is it due to fuzziness in trying to observe objects at vast distances? And could we resolve or at least refine this "not much difference" with the new telescopes now on the drawing board? In the current Scientific American there's an article on them, and the striking thing is the huge increases in the diameters of the main mirrors.

10. May 9, 2006

### ptalar

So, if I understand the discussion correctly the Universe is:

1) Expanding faster than the speed of light and since it expands into nothingness no laws of physics needs apply in nothingness. So that is why we can see back to 46 billion light years.

or

2) The universe is spherical and we are on the surface of a spherical balloon so we can see distances along the surface of the universe between two points that are greater than the actual radius, if there is one. Also, the speed of separation on the surface is much greater than along the radius.

I am just trying to get a physical feel of what is going on rather than being buried in equations.

Any thoughts?

Phil

11. May 9, 2006

### hellfire

If space were static and you would send a photon at t = 0 and wait until t = 13.5 billion years, you would afterwards find out that the photon is 13.5 billion years away from you. In an expanding space things are different. You sent a photon at t = 0 and wait unil t = 13.5 billion years. The photon has travelled 13.5 billion light-years because it travels always at same speed. However, it is not located at 13.5 billion light-years from you, but farther away, because between you and the photon space has expanded in the meanwhile. This has nothing to do with superluminal expansion neither with the geometry of space.

Last edited: May 9, 2006
12. May 9, 2006

### hellfire

This is right. Between z = 0 and z = 50 you have 40 billion light-years in the standard cosmological model, and the remaining 6 billion light-years are between z = 50 and z = $\infty$.

13. May 9, 2006

### ptalar

Hellfire,

I understand what your saying. Sort of like my expanding sphere or balloon example above in part 2. The balloon is expanding and the observer and the photon are also moving apart on the surface of the balloon. But 46 billion light years? How can we see back 46 billion light years (the observable Universe) if the Universe is only 13.7 billion years?

Phil

14. May 9, 2006

### Hulse

Anybody,

Let’s run the cosmic clock backward from now till the big bang.

Let's blow a balloon up such that the radius from the center of the sphere is r=14 meters. Each meter corresponds to 1 billion lightyears. All over the outer surface of the balloon we affix silver beads spaced roughly equidistantly apart. Each bead G represents a galactic cluster.

We choose two beads, G1 and G2, and measure the distance d between them. Now we proceed in steps. First, we let air out till r=13 meters and measure the distance between G1 and G2 and get d1. Second, we let air out till r=12 meters and measure the distance between beads G1 and G2, and get d2. Third, we let air out till r=11m and get d3. We repeat these steps till r=0m, which represents the big bang.

Note that the process can be continuous rather than just stepwise, with continuous measurements. Note also that the speed of the balloon’s shrinkage can vary, even to the point that inflation (backward) can be a very sudden event. One can then reverse the process, run the clock forward from r=0 till now to represent the history of cosmic time. Note also that I choose to use beads rather than to buy those balloons that have the galaxies already printed on the surface, because those printed galaxies shrink as the balloons shrink, but the beads don’t.

Question: Is this a good model to use in my presentation to my discussion group? The group is made up largely of MDs and biology PhDs who give the appearance of knowing everything, but who really know next to nothing about cosmology (though they’re all nice people). We have only one physicist, who’s mainly into computers, but who can easily call my bluff if I make one. (So I don’t want to bluff or make mistakes.)

Thanks.

15. May 9, 2006

### Garth

Hulse the model of a balloon is only an analogue for the spherical GR universe, in which case the radius of the balloon is not time, you need that to be independent of your model so you can still blow it up! (Movement requires time)

If you want to identify the radius of the balloon with time the model becomes static, like an onion with many layers, but that radius is not atomic time in GR rather it is conformal transformation of atomic time. The expansion is not linear, except of course in the linearly expanding or “Freely Coasting” Cosmology when the radius is atomic time!

Garth

Last edited: May 9, 2006
16. May 9, 2006

### ptalar

I believe we are so wrapped up in theory than we are beginning to lose all sense of reality as we are living in the hear and now. The visible Universe is 46 billion light years, conformal transformation of atomic time, its all theory made to make the math work with no experimental proof. The only way we can see distances equal to 46 billion light years away is for the expansion to occur faster than the speed of light. There is no law in physics to stop that since at the edge of the Universe you are essentially at the beginning of the big bang and the laws of physics break down at the moment less than the planck time of so many 10 to -46 seconds after the big bang. You are also expanding into nothingness where there is no law that states you can't go faster than light.

Anyway, I am just a lowly mechanical engineer trying to come to a better understanding of cosmology. Maybe I am way off but I enjoy the collegial talk. Thanks for sharing.

Phil

17. May 10, 2006

### SpaceTiger

Staff Emeritus
An object can recede from us at greater than the speed of light if its recession is due to the expansion of space itself, rather than its motion through space. This doesn't have anything to do with the breakdown of physics near the big bang.

18. May 10, 2006

### pervect

Staff Emeritus
As various people have remarked, the baloon model is good for a spatially curved universe. But current cosmological models have k=0.

Therfore a slightly better model is just to imagine a planar rubber sheet in a frame - using your balloon idea, but with a planar balloon. The rubber sheet is stretched out by enlarging the frame by the scale factor of the universe, which is a function of cosmological time. This is usually called a(t).

On this rubber sheet, draw a circle, which we call the obsevable universe. Outside this circle, signals travelling at the speed of light could not reach us or any event in out past. This region is intrinsically unobservable to us at the present time, therefore it is a matter more for philosophy than science. Explain that you're not going to speculate about what lies outside the circle.

Some interesting plots that I'd have to think about how to draw:

What we can observe, in the future, if we stay put

What we can observe, in the future, if we set out at velocity v in some particular direction.

What we could eventually learn about from other observers who have also been studying cosmology if we eventually develop sublight interstellar travel and meet them someday.

Slightly inside the circle, draw another circle, which is the surface of last scattering. This is the region that we can actually see, due to the fact that in its early history, the universe was opaque. The CMB originates from this circle. Explain that we have a lot more information about events inside this circle than the previous one, as we can not directly "see" beyond the time when the universe went opaque. But we have some information from this period, based on things like isotope concentrations that we don't have to actually "see".

Switch from the baloon model to graphs to illustrate the shape of a(t), the stretching factor as a function of cosmological time.

Draw the path that light takes in cosmological coordinates, and illustrate how a switch to conformal time can make the light cones straight and easy to draw.

Write down the equation

ds^2 = a(t)^2 (dx^2 + dy^2 + dz^2) - c^2 dt^2

and explain that this is the equation that motivates all of the diagrams you've presented.

Last edited: May 10, 2006
19. May 10, 2006

### pervect

Staff Emeritus
We certainly know more about things we can actually see directly - things inside z=1100 - than we do about things outside this region.

However, it is not true to say that we know nothing about things beyond this. Things like isotope concentrations tell us a little bit about the earlier history of the universe. They tell us enough about this period that a lot of cosmological theories can be and have been thrown out because they don't explain the observations properly.

Some of our cosmology comes from assumptions. One of the most important assumptions is that GR is a good theory of gravity. People can construct other theories of gravity (such as Garth's SCC) - but these theories make predictions that we can test now (and in the case of SCC, are testing, with Gravity probe B).

We will certainly feel more confident that we fully understand gravity when we have a better understanding of dark matter, dark energy, and related issues. Perhaps a fuller understanding of these issues will change our cosmological theories, so there is certainly some potential room for change as we gain more knowledge about these areas.

The fact that there are some things that we may not fully understand is what makes cosmology an intersting and exciting area. Progress is made by writing down theories that actually make predictions, and testing them. Modern cosmology does a good job of making a LOT of correct predictions. Progress is not made by throwing up one's hands and declaring the universe unknowable.

Nope. A lot of people get confused over this issue. The simplest way to think about it is that the distance we are measuring "now" is not the same as the distance that light travelled - because space expanded in the meantime.

There are more subtle aspects to the issue as well, but I've found them uniformly hard to explain :-(.

20. May 10, 2006

### Hulse

Well Garth,

You popped my balloon. I'm having a difficult time visualizing this model. I looked at the two journal articles you mentioned, but haven't had time to read them completely yet. It takes me a long time to puzzle through.

I need to comprehend "atomic time" and "conformal transformation of atomic time." I understand, I think, the freely coasting universe as not being accelerated by "dark energy." Isn't it like the difference between a spacecraft shot into space by an electromagnetic accelerator versus one accelerating into space under the power of its own rockets? But at this point I don't understand the difference between "atomic time" and "conformal transformation of atomic time" at all.

Hulse

21. May 10, 2006

### Garth

Hulse - Atomic time is that measured by an atomic clock. In a spherical universe (GR with $\rho_{total} > \rho_{critical}$) the radius of the hypersphere is described by the scale factor R(t) and is not equal to the atomic age of the universe, but a function of it. Only in the linearly expanding universe are the two identical: R(t) = t R(t0)/t0.

To clear up any confusion: GR models expand or contract. The gravitational field or in other words, the gravitational forces between objects in the universe, cause that expansion to decelerate. (Like your coasting spacecraft slowing down under gravity) If the universe accelerates in its expansion then dark energy is required, as is the case with the modern standard $\Lambda$CDM model.

If the universe is empty then it linearly expands as there is nothing to slow it down. If however there is matter in the unverse and in a particular model the expansion is still linear then some form of 'dark energy' is required to counteract the deceleration of the internal gravitational forces. In SCC that is provided by the scalar field.

The term 'freely coasting' is not mine but comes from a team looking at a model in which the universe behaves as if it were empty, even though it is not. In that model some unknown mechanism causes the universe to behave as if it were free of the gravitational deceleration of the GR models.

Note one difference between Freely Coasting Cosmology (FCC) and SCC (apart from the SCC identification of that mechanism with an interactive scalar field) is that the FCC universe has negative curvature (like the Milne model) whereas the SCC universe has positive curvature.

Garth

Last edited: May 10, 2006
22. May 10, 2006

### ptalar

Space Tiger, Pervect,

Thanks for your replies and thoughts. This is definitely not a simple subject. But it is fascinating. I am pondering what you have said and will get back with you.

thanks,

Philin

23. May 10, 2006

### pervect

Staff Emeritus
One point I made a bit tersley that I'd like to expand. The equation

ds^2 = a(t)^2 (dx^2 + dy^2 + dz^2) - c^2 dt^2

is the key to understanding the flat expanding universe. x,y,z,and t are so-called "co-moving" cosmological coordinates. This means that a galaxy typically has x,y, and z constant if it is "moving with the flow". The galaxy then moves along a line of varying t, cosmological time.

So, we understand galaxies, and how they move. (They basically don't move in these coordinates, they stay still). The next things we need to discuss are how light moves in these same coordinates. When we know how galaxies move, and how light moves, we can work out what we actually see.

Light moves in such a manner that ds^2 = 0. You can easily see that the "slope" of light is not constant in these coordinates, that the slope depends on a(t). If y ou look at ned wright's cosmology tutorial, you should be able to find graphs showing the path that light takes, and little "light cones".

there are a few other things that are useful to know, but these are probably the two most important.

24. May 10, 2006

### Hulse

Pervect,

Your rubber sheet analogy is extremely helpful. I think even my egotistical MDs would be impressed, if I'm able to convey it to them properly. They don't have time to learn this anywhere else, and they love the discussion group, because those of us who make presentations are very careful to prepare.

At my last presentation I used the "spatial hypersurface" illustration of tangent circles, each one nearly identical to our own observable universe and circumscribed by the surface of last scattering.

One physician, who normally is very skeptical of everything outside his own field (quality of instruction to medical students), took my paper away with him and showed it to a physicist friend (may have been a cosmologist, he didn't say) of his to see how well I did. He came back the next meeting and said his friend said I did a "good job." This greatly impressed my skeptical physician friend, who just retired from a long career as a prof in our university's school med).

But I'm glad I came here, because I was going to do the "shrinking balloon" analogy, but after you guys I'll spare myself the embarrassment.

The "rubber sheet" analogy is excellent for my purposes, because it can be readily understood by specialists in other fields who have no time to mess around with science reporters who don’t do their homework.

So thanks, and I'll be back later with more questions.

Hulse

25. May 11, 2006

### Hulse

I have another problem I need help on.

Assume that the standard model is correct but incomplete. In your imagination you are an immortal being. Like a mathematical point, you have no spatial or other physical dimensions. Mass/energy = 0. Length = 0, width = 0, height = 0. In these respects you are like religion’s idea of the immortal human soul or God or a god. Or, in non-religious terms, you are an intelligent, mobile viewpoint capable of observation. You can see, hear, touch, feel, smell, taste, think, remember, make decisions, and so on. You also have extraordinary powers. You can move forward or backward in time at any rate, including instantaneous. You can stop in time, make observations, then continue on at the normal rate of time we observe today. You can cross all dimensions. Quantum effects don’t bother you. You can go into and come out of a black hole. You are immune to all extremes of heat, pressure, etc.

You decide to go backward in time starting from the here and now. Your destination is the big bang.

The galaxies appear closer and closer. Everything closes in on you. You enter the Planck epoch. Everything we observe in our “observable universe” of today is compressed a billion times smaller than a proton. Time has no definition.

Questions: What then is the “observable universe”? How can the “observable universe” be distinguished? Where is the cosmic horizon? Does quantum tunneling exist?

So-called common sense would dictate that in a compression so small, a billion times smaller than a proton, there would be “an inside” and “an outside” and that “the inside” could be distinguished form “the outside.” But in this imaginary situation, common sense has no value. This is so because humans have no “common experience” from which to form a “common sense.”

Therefore I will rely on the “uncommon sense” of the good folk of Physics Forums.

My thoughts here were formed by reading Fred Adams’ 2004 “Our Living Multiverse.” He seems to be able to distinguish and talk about an “observable universe” with physical properties. And yet, if there were no “observable universe” to distinguish because there is no boundary, how can he even talk about big-bang physics?

Most folk in my discussion group (remember they’re almost all professionals with MDs, PhDs in the sciences, and some in the arts/humanities) assume that the big bang began in a point inside of space and that the observer could be outside watching it like you would watch a fireworks explosion in the night sky on the Fourth of July. And if I challenge this assumption, they ask me to prove them wrong.

Can anybody here help me? How do I convince them that we are right now inside and not outside the big bang and that if we run the cosmic clock backward we could not observe it from a point outside it?

Your indulgence is requested for any misconceptions I may have expressed above.

Thanks,

Hulse