How Vast is the Cosmos?

by Robert Lawrence Kuhn (9/27/10 8:55 pm)

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Since childhood, I’ve wondered about existence—what is it all about? Now, having explored many things but being no surer (and feeling no smarter), I start anew. Is there anything of transcendental knowledge, I ask myself, which I can know for sure?
For me, it’s the enormity of the cosmos. It stops my breath.
Everyone knows that the universe is huge, but no one could have imagined how incomprehensively immense the universe, or multiple universes, may actually be. Physicist Alan Guth, who revolutionized cosmology with inflation theory—which describes how space expanded exponentially in a fleeting fraction of a second and culminated in the big bang—believes that our universe is at least 10²³ times larger than our observable universe (because inflation requires at least 100 doublings). This means that our universe, which Guth calls a “pocket universe” (defined as an entity whose space all inflated together), is 100 billion trillion times larger than everything we can see with our largest telescopes.
All the vast expanse of our visible universe is but an insignificant speck in Guth’s inflating universe, which itself is only one pocket universe among an innumerable or even infinite number of other pocket universes. In almost all theoretical models, once inflation starts, it never seems to stop because the inflation-driven expansion of space is always faster and greater than the local decays into pocket universes.
If, indeed, the cosmos is unimaginably immense, the person who has given us new eyes to see it is physicist Andrei Linde, who dramatically expanded the power and significance of inflation theory. Linde’s universe grows chaotically and eternally. When he was first studying inflationary theory, he came up with numbers like 10⁸⁰⁰ or 10^1,000 for estimating the degree to which the real size of the universe is larger than its apparent size (i.e., the observable universe), and he was always apologizing (in those early days) for the seemingly absurd scales. Then, his continuing work led inexorably to the wild and putatively outrageous idea that the size may be 10^1,000,000 or 10^{1,000,000,000} larger than we can see. That’s a billion zeros to define the extent of our universe, a billion orders of magnitude larger than our observable universe, a number that is so large it has no name. (Remember, the number “1 billion” has only nine zeros; this number has a billion zeros.)
Here’s how the enormity of the cosmos really hit me. When, some years ago, I first read Linde’s papers, I was frustrated because he never seemed to use units of measure when giving these numbers. It wasn’t 10^1,000,000 “meters” or “centimeters”; it was just a naked 10^1,000,000. Finally it hit me—with a wallop. Units don’t matter!
What, units don’t matter? That sounds ridiculous, but that’s right, and here’s why. What’s the largest possible unit of measure that we can use? How about the radius of the observable universe, which is approximately 10²⁸ centimeters? What’s the smallest possible unit? How about the Planck length, which is approximately 10^-33centimeters? Now, what’s the order of magnitude of the difference between the largest possible and smallest possible units? The answer is obvious: about 10⁶¹. That’s 10 trillion trillion trillion trillion trillion. This means the observable universe is about 10⁶¹Planck lengths.
How does this number match up? No matter its obvious immensity, 10⁶¹ isn’t even a rounding error, not even a micro-speck, when compared to 10^1,000. When compared with 10^1,000,000or 10^{1,000,000,000}, 10⁶¹ (or 61 orders of magnitude), the unit extremes of our universe, are utterly insignificant. Far, far, far less than a single grain of sand compared to all the sand on all the lands on all the planets in all the (observable) universe. Whether the units are radii of the universe or Planck lengths will have no impact on these colossal numbers. It was when I got this point—that human kinds of units are immaterial when contemplating cosmic vastness—that I began to realize how really vast the cosmos may be.
This is only the beginning of cosmic immensity. Linde began to realize that inflation may be “eternal,” meaning that inflation will forever create new universes of immense size. If so, this would mean that our universe, whether 10^1,000 or 10^{1,000,000,000} times larger than we can see, is still only our own “balloon universe,” the one in which we find ourselves, the one among many. The entire cosmos would be an infinite collection of such balloons, an infinite number of gigantic universes.
It is enormity beyond comprehension. I am overwhelmed. But still it doesn’t end. Physicist Max Tegmark suggests there may be other ways reality has become unimaginably larger and that truly “parallel universes” may really exist. The most famous mechanism is “quantum branching” in the many-worlds interpretation of quantum mechanics, where at every observation or at every tick of Planck time (approximately 10^-44 seconds), all reality splits into parallel worlds. The permutations become staggering. Not yet content, Tegmark goes further still and suggests that perhaps every kind of consistent mathematical structure, which forms the fundamental laws of physics, may actually exist and generate complete worlds (even if most are empty or simple).
Put simply, whatever can exist, does exist. Harvard University philosopher Robert Nozick called it “the principle of fecundity” and Princeton University philosopher David Lewis called it “modal realism.” Going all the way out, Lewis said: “I advocate a thesis of plurality of worlds, or modal realism, which holds that our world is but one world among many. There are countless other worlds…so many other worlds, in fact, that absolutely every way that a world could possibly be is a way that some world is.”
Now note this carefully: All of Guth’s infinite “pocket universes” and all of Linde’s infinite “balloon universes” are, taken all together, but one of Tegmark’s vast number of “mathematical worlds” and but one of Lewis’ “plurality of worlds.”
Do unlimited worlds make sense? I’d probably go with physicistPaul Davies who says, “two cheers for the multiverse.” He is prepared to accept that the cosmos is significantly larger than the totality of what we see, that there may be other regions of space and time different from what we observe, “other universes if you like.” But he does not believe that “all possible universes are out there,” which he says would be “contradictory and absurd.”
So, how vast is the cosmos? Whenever we’ve set its limits, it was always too small. The cosmos didn’t change, of course, but our feeble vision of it surely did. The more we learn about the cosmos, the larger it becomes, and the smaller we seem. But, perhaps, for one thing: We understand it and we marvel at it.
Anyone contemplating the big questions of existence must confront the staggering size of our universe and the real possibility of multiple universes without number or limit. This is not science fiction; this is our cosmic home. Simply appreciating the ineffable enormity of the cosmos is already closer to truth.

 

Tags cosmos, vast, Guth, Linde, Rees, Tegmark, Nozick, Lewis

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