Monday, March 06, 2006

Inflationary Difficulties

"Cosmic Inflation" is the theory that the early universe expanded in size exponentially. To my mind the theory is suspicious because it is used to justify the idea of a continuous creation of "pocket universes," as Alan Guth, the theory's originator calls them—as if the universe were as casual an occurrence as clearing one's throat. I'm not a theorist, so I'm not qualified to discuss the mathematical merits of the relevant theories, but I do think Inflation's philosophical consequences signal the need for scrutiny of its philosophical assumptions.

Inflation finds its justification in three "problems" of cosmology: the Monopole Problem, the Flatness Problem, and the Horizon Problem. I will review each of these in turn, but will only treat the last at any length.

The Monopole Problem is simply that no one has ever found any magnetic monopoles ("lack of any observed topological defects" is how Wikipedia puts it). To most of the world this doesn't seem like much of a problem, but since many grand unified theories (GUTs) require the existence of monopoles, the universe of our experience doesn't suit the theories' creators. (I presume that monopoles still plague the latest batch of GUTs, but perhaps it is only my ignorance that prevents me from seeing why monopoles need otherwise inhabit every generation of such theories forever.)

The Flatness Problem is the inexplicably Euclidean (or flat) geometry of the universe. That is to say, that the angles of cosmic-sized triangles sum neither to more than 180 degrees as they do on the surface of a globe, nor to less than 180 as they do on the surface of a saddle, but to exactly 180 degrees as on a flat piece of paper. As Goldilocks would say, "Just right."

The Horizon Problem is the large-scale homogeneity of the universe: that the universe at a particular period of its expansion was too large for influences propagating no faster than the cosmic speed limit (the speed of light) to smooth its mass and temperature inhomogeneities, in other words, that parts of the universe would lie outside the "horizon" of physically accessible points from each other.

This "problem" has never been adequately explained to me and always nagged me as the flimsy. If, I thought, the universe started as a singularity (essentially a geometric point) as the Big Bang theory tells us, why would the horizon problem be an obstacle? For that matter, why would a limit on any influence be an obstacle?

The issue finally bubbled up to top of my priorities, so I looked it up in Alan Guth's Inflationary Universe. Here's what he had to say,

The horizon problem is not a failure of the standard big bang theory in the strict sense, since it is neither an internal contradiction nor an inconsistency between observation and theory. The uniformity of the observed universe is built into the theory by postulating that the universe began in a state of uniformity. As long as the uniformity is present from the start, the evolution of the universe will preserve it. The problem, instead, is one of predictive power. One of the most salient features of the observed universe—its large scale uniformity—cannot be explained by the standard big bang theory; instead it must be assumed as an initial condition.

The reasoning may not be apparent to you, but at this point in my intellectual development, I found it quite indicative of the modern scientific mindset—so indicative in fact, that I might not be able to unpack all it communicates in this one post.

On reading this paragraph, these questions rushed to mind: Where would inhomogeneities originate? Wouldn't they require explanation?

But that is not how the modern scientific mind works. The whole push is to show how the current state of affairs and no other is possible. Applied to the horizon problem, this means that no matter how the universe began, whether homogeneous, or completely inhomogeneous, it would coverge to homogeneity of itself.

On one hand, it is difficult to argue against this motivation. Science seeks naturalistic causes, that is, causes lying solely within the realm of the created world.

But on the other hand, eventually science must fall silent. The beginning of the universe seems an appropriate point. Science has to admit its limitations and simply accept the reality of the world as given. That is what it means for experiment to be the touchstone, after all.

To a certain extent, inflation theory and all physical theories do this: the theorists merely fold up more of the world into their theories, but they never explain where the theories come from. Of course, the claim is that someday String Theory or its successor will produce a self-explaning mathematical theory of everything.1 What that means is not very clear. No one can point to an example of a self-explaning mathematical theory for anything, or even explain how it would explain itself. But it's clear it can't mean the theory is obvious, because then we would have discovered it long ago. Perhaps they mean the theory is obvious in retrospect, as in "I should have known." Still it takes human minds to create theories, and it's hard to see how the theory could also create the human mind without indulging in circular reasoning. And as Stephen Hawking in the one lightning bolt of philosophical lucidity in his A Short History of the Universe asks, "What is it that breathes fire into the equations?":

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire in the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Ot does it need a creator, and, if so, does he have any other effect on the universe?2

Also of interest:

  • Nothing Comes from Nothing
  • Can You Bind the Chains of the Pleiades?


    1. As always "The check is in the mail," arriving perhaps about the same time that Marx's dictatorship of the proletariat brings us to utopia and surrenders power.

    2. Hawking's philosophical muse clearly abandoned him for the last line of the paragraph: "And who created him?". I have left it off for brevity sake but will take it up in a future post.

    Alan Guth, The Inflationary Universe (New York: Addison-Wesley Publishing Co., 1997), 184.

    Stephen Hawking, A Brief History of Time : The Updated and Expanded Tenth Anniversary Edition (Bantam, 1998), p. 190.


    Jon Jackson said...

    Maybe you could explain something to me: If the universe essentially started out as a massive black hole and the escape velocity of a black hole is greater than the speed of light then how did the universe start seeing that nothing can go faster than the speed of light?

    Lawrence Gage said...

    Where did you hear that the universe started essentially as a (massive) black hole? From my understanding, that's a rather poetic use of the term "black hole."


    Steve said...

    Jon said,

    "Maybe you could explain something to me: If the universe essentially started out as a massive black hole and the escape velocity of a black hole is greater than the speed of light then how did the universe start seeing that nothing can go faster than the speed of light?"

    It's funny you say that! I was lying in bed last night pondering the same thing after reading LG's post on Cosmic Inflation. I don't fully understand the technical problems with the Big Bang that lead to Inflation Theory, but it did get me thinking that without the exponential growth in size/speed the whole thing would not even escape itself in the first micro second. The density of the entire universe wrapped up in the head of a pin would be the mother of all black holes.

    Now this has me thinking, if the inflation increased in the order of X to the power of 50 or more, even for a few seconds, how many years do we need to subtract from our existing 15,000,000,000 estimated years since detonation.

    Lawrence Gage said...

    I'm not sure why you two think the universe started as "a black hole": perhaps the word "horizon" reminds you of the event horizon of black-hole fame?

    The general relativistic metric (the mathematical form that describes how spacetime bends) for a black hole is significantly different from that for the universe. I'm not a relativist, but perhaps it's not too far off to put it in these terms:

    black hole = mass within event horizon surrounded by space

    universe = mass not surrounded by anything at all (that is, not embedded in a larger space)

    The "big bang" is the initial impetus that caused the expansion. As Guth himself says, inflation isn't necessary for the initial expansive motion. The term "big bang" is unfortunate; it was devised by opponents of the theory and makes it sound like an explosion into a larger space, but it was probably more like an opening flower or matter falling upward, so to speak: a natural, non-violent motion. (The metaphors fall short because there's really nothing that's a very exact comparison to "the sum total of all physical interacting things," that is, the universe.) The universe doesn't have to worry about climbing out of an event horizon, because it's the space itself within its horizon that is expanding: the "boundary" of the universe simply gets bigger as it expands.

    I hope that's helpful.

    Steve, Guth says on the same page of the book that the theories with and without inflation describe indentical cosmic radii for all times after 10^-35 seconds. In brief, inflation makes only the smallest fraction of a second of difference in cosmic age, certainly well within the uncertainties of its measurement.


    Jon Jackson said...

    So you're saying that space, as well as everything else was expanding at the same time so there was no contradiction?

    Lawrence Gage said...

    No, I'm saying you're "comparing apples to oranges." The universe is so entirely different from a black hole that the analogy you're trying to use doesn't fit. Most significantly, the universe doesn't have anything to "escape" into. Perhaps more immediately preceivable: in a black hole the only direction you can travel is down, whereas clearly you can travel in every direction in the universe.