Size of the Universe Part 2

Building on Part 1, I put this page together to describe how the universe is put together on a cosmic scale. I think the first part of this project was probably a cakewalk in comparison, but do we climb mountains because it is easy or because it is hard? Actually, I’m just fine hanging out on level ground, but anyway, it sure helps to have an interest in science and also having read a few books on quantum mechanics and Einstein’s theories.

Note: Except for the age of the universe, all other calculations on this page are based on 2010 estimates, and may differ slightly from the current concensus.

Speed of the Universe

The present theory is that the early universe underwent a period of rapid expansion known as cosmic inflation. After a relatively quick slowdown, the universe settled into a more graceful rate of slowdown until about 5 billion years ago, when it stopped slowing altogether. This does not mean the universe stopped expanding, however. And there is current evidence to suggest the rate of expansion has since been accelerating.

Similar to the speed of gravity, when it comes to applying a speed to this expansion, one cannot really apply a specific speed as we do to say, a car traveling between two points, or a planet’s orbiting velocity around its sun. There is simply the speed at which two objects in the universe are moving apart from one another at a particular distance. Two galaxies say, one million light years apart (if not bonded by gravity) will be moving away at one velocity, while two galaxies two million light years apart will be moving apart twice as fast. There is a formula for calculating an objects recession velocity, and that is known as the Hubble Constant. The Hubble Constant has changed over the years as scientists have used new methods of figuring out the average speed that galaxies are moving away from us at a particular distance. At present (10/10) the Hubble Constant is estimated to be about 70km/sec/mpc (70 kilometers a second per megaparsec) depending on whom you ask. I wouldn’t be surprised if that figure becomes outdated a week from writing this, and as previously noted, the expansion rate of the universe appears to be accelerating. As a result, I think a better name for the Hubble Constant would be “The Ever Inconstant Hubble Constant,” but that is one person’s opinion.

As noted in Part 1 of this project, the size of the universe is not known, only the size of the universe that we can see. As far as the visible universe is concerned, then, the two farthest points away from the earth in any direction--directly across from one another--are moving away from each other at the fastest speed. If the visible universe represented the entire universe, one might call this the ultimate speed of the universe. The current recession velocity of the matter that produced the CMBR is a whopping 3.33 times the speed of light--if my math is correct. This means that although we can only see the dispersion of matter that produced the CMBR as it was 13.8 billion years ago, the old galaxies which that matter has theoretically condensed into are presently moving away from us at an average 3.33 times the speed of light in accordance with galactic recession. Multiply that by two, you get a figure of 6.66 times the speed of light--the ultimate speed of the visible universe. Wow, now there is one for the superstitious.

The fact that two very distant objects are moving apart from one another at sometimes incredible velocities is the same reason that two objects can be moving away from one another faster than the speed of light, yet still recieve light waves from one another. I think the little animation at the top of this web page I discovered is about the best example I have found showing how such a thing is possible, although there is still room for improvement: It does a good job explaining the aforementioned concept, but does not illustrate the stretching effect that the expansion of space has on light.
The Distance Scale of the Universe

Bear in mind that locally, for any hypothetical inhabitants at the edge of the visible universe, conditions are very likely the same as for us. And just like us, the expansion of the universe exerts a small force on the atoms making up their planet. But just like the Earth, the force is not enough to overcome the attractive forces of nature. So just as the Earth, the solar system and the Milky Way remain a constant size, so do objects in their part of space. And, of course, they do not perceive themselves as moving six times the speed of light. Like a raisin being carried along in a baking loaf of bread, their galaxy is moving along with the space in its vicinity, just as ours is.

Now I do not have 100 percent confidence in my math, so don't take my word exclusively; but out of curiosity, and after some serious calculation, I managed to figure out how fast space is expanding at the local level. As it turns out, the velocity is pretty slow: The space between the Earth and Sun expands about one centimeter every hour. But as previously noted, that doesn't mean that the Earth grows one centimeter farther from the Sun every hour; gravity is the force that wins out at this scale.

The following diagram shows the relative size of the visible universe from the time the CMBR was emitted. As you can see, during the first 2.7 billion years, the universe expanded some 426 times, but only expanded twice its size during the next 5 billion years; and from 5 billions years ago to the present, only 1.5 times in accordance with the prevailing theory.

Shape of the Universe

As mentioned in Part 1, the shape of the universe is not known with absolute certainty, but we are going to assume it is spherical for the sake of argument. Now, don’t shoot the messenger, but in regards to a hypothetical spherical universe, our spherical universe could also be said to be flat. Yes, you read that correctly. Ask any astrophysicist type what the shape of the universe is and they will likely answer your question only in terms of a shape that takes the dimension of time into consideration. Historically, there were only three shapes, a sphere, a flat two-dimensional surface, and a saddle, but new ones have been added, which I don't think I could explain if I did understand them. However, to the best of my understanding, the three aforementioned shapes are meant to depict all of space as a two-dimensional membrane, stretching in time: A universe that expands, only to collapse back in on itself, would be the sphere; one that expands forever--its fringes expanding outwards faster than its core--would be the saddle; and one that halts to near zero expansion would be the flat surface; at least, that was the thinking at one time. (rev 11/17/18, 1/19/20)

As mentioned, the current consensus is that expansion is accelerating. In other words, the force driving expansion is not weakening to the degree everyone assumed it would. But, lo and belhold, the universe can still be flat, as the accelleration appears to be evenly distributed throughout the entire universe. (rev 1/19/20)

For the average person, though, who might be attempting to visualize the universe, my advice is to ignore such shapes. You might spare yourself a headache or two in the process. Suffice to say that gravitational fields warp space; they slow time, bend light and, of course, attract other objects. So it has long been postulated that gravity might have a large-scale effect on the entire universe. Be aware of one thing, though: When cosmologists describe a particular model of space-time as being infinite, they typically mean that the universe--if agreeing with that model--will go on expanding forever. (rev 1/19/20)

Center of the Universe

In the not-so-distant past, a lot of scientists still viewed the recession of galaxies as if the Earth was a more or less stationary object at the center of the expansion. So because Einstein’s Special Theory of Relativity predicts that motion through space slows time much like a gravitational field, they imagined that time slowed down more and more for those galaxies that were farther from the Earth, and they even took it into account for calculating their distance. Scientists currently view the universe much differently: The presently accepted view is that space itself is what is expanding, and we are just along for the ride.

So where is the center of the universe? Again, to any astrophysicist type who is only concerned with calculating a particular object's position in the visible universe, the notion of the universe having a center has no particular relevance. That doesn't mean that a three-dimensional center does not or can not exist. At one time, I rather naively envisioned the Big Bang using common frames of reference such as a firecracker explosion or perhaps a jet of water from a garden hose. In the case of the firecracker explosion analogy, you would simply try and look for the void left behind by the explosion. In the case of the garden hose analogy, you would look for a certain direction where things were denser to find the center of the universe. Both concepts are terrible analogies for describing the universe, however. The fact is, when you are part of an expanding medium, attempting to locate the center of that medium might just be impossible. No matter where you look, or where you look from, everything is pretty much the same. The universe appears to be evenly dense (on a cosmic scale) no matter where you look or where you look from. And the most distant galaxies are all moving away at the same average rate for a given distance no matter where you look or where you look from. To illustrate more clearly how such a thing is possible, I created the following diagram. The “bicycle spokes” represent galactic trajectories. The diagram is based on the visible universe being part of a larger universe concept depicted in the last diagram in Part 1. The Milky Way, then, is galaxy A, but galaxy A could represent any galaxy in the universe as far as the principle is concerned. Galaxies C and E reside at the fringe of the visible universe. Now, if you take the time to measure the distances between galaxy A and the other galaxies in both the past and present visible universes, you will notice that galaxies C and E have moved away from galaxy A twice as far, and therefore twice as fast, as galaxies B and D. This is exactly what we see in the recessional (cosmological) redshift of galaxies as we look out farther out into space.

There are three ways in which light waves from distant objects can increase or decrease in frequency: The first item we will deal with is cosmological redshift: The expansion of the universe, as depicted in the above diagram, can only decrease the frequency of light. Measuring it might be problematic, but for a given distance at any moment in time, this velocity is very precise for the entire universe. Next, the Doppler effect: So you look up at a distant galaxy with your telescope, calculate its cosmological redshift and determine its exact distance using the Hubble Constant, correct? Not exactly; the frequency of the galaxy’s light waves could be increased or decreased by either its own motion through space, or by the Earth's motion. So knowing the Doppler shift of any distant object will always yield a more precise distance calculation. And lastly, gravitational redshift: As a lightwave leaves a star, the star's own gravity can stretch the light wave, thereby reducing its frequency, although for most stars, this is a slight effect, until you get into very dense objects.

In the science fiction movie Star Trek, The Final Frontier, the starship Enterprise is hijacked on a quest to find the center of the galaxy. In reality, the center of the galaxy looks to be the domain of a very large black hole--probably not a good place to plan the holidays. The center of the visible universe is, of course, the Earth. And although the odds are astronomically against it, the Earth could be the center of the entire universe. The point being that wherever the center of the universe may be, whether nearby or perhaps a trillion light years away, there would not be anything particularly special going on there. It would only be a geometric location that you could point to and say, “That is the center,” if it were possible to know its location.

This page was assembeled with marginal help from N. Wright, T. Davis; with a little more from C. Seligman.



mysteries, commentary, sci-fi

10-24-10, last rev = 2-10-20

2010 Dave Conklin