Monday, October 17, 2005

The best Fine-Tuning in all of Physics

In preparing to give two cosmological ID talks this week, one in Maryland and one in Virginia, I tried to find a way to explain the fine-tuning in the cosmological constant, denoted by the Greek letter Λ. It's not very easy: the fine tuning of the cosmological constant is not expressible in the normal manner.

The normal way to express a fine tuning is to say that if this physical constant (pick one) is varied by just a small amount, then life could not exist. While that is true for Λ, it is also true that in this case the situation is more complicated (and more dramatic.)

We have to start with a little cosmology. In particular, two amazing discoveries of the last fifteen years.

The first is that the universe is flat. Among other things, that means Euclidean geometry will be accurate, even on cosmological scales. If you think of the surface of the earth as a 2D universe, then the earth is "fairly" flat, meaning that the curvature is so small that it is hard to detect. The Little Prince, on the other hand, lives on a highly curved planet.

The second amazing discovery is that the universe is not only expanding, but the expansion is accelerating.

Both discoveries, but more transparently the second—accelerating expansion—point to the need for an anti-gravity force in the universe. If the universe were contracting or its expansion slowing, then there might be some way out of anti-gravity. But there is no way out with an accelerating, expanding universe.

An accelerating, expanding universe also crushes the hope of some that the universe is oscillating. An oscillating universe was sometimes expressed as a way to restore a kind of steady state. It never really worked, because even if the universe did oscillate between big-bang and big-crunch, it still has to pay the piper in the form of the 2nd Law of Thermodynamics. The oscillations would die out, a fact that implies not only an end to the universe but also, once again, a beginning.

Λ Plays a Big Role

Observationally, it appears that matter accounts for 30% of the universe, and the anti-gravity component, whimsically known as "dark energy", accounts for a whopping 70%.

The cosmological constant Λ represents a vacuum energy density (the energy present in "empty space") that, if positive in sign, enters into Einstein's General Relativity as a anti-gravity force. This then provides a natural way to explain dark energy.

Here is the problem. When the best and brightest calculate Λ they get what turns out to be a very large value. For convenience, let's choose a system of units where this calculated value is 1.

Here we take a detour into physics psychology. For a long time, prior to these recent observations, it was known that the calculated value for Λ was way, way too big. However, it was believed that the actual value was probably identically zero. Now this discrepancy, a big calculated value versus an actual value of zero was, in a way, no big deal. Physicists are used to this—and expected the explanation to come in some form of super symmetry—an elegant explanation from first principles that Λ had to be exactly zero.

Now, however, we face a very different picture. Λ is now invoked to explain the dark energy. It cannot be zero. It must be a positive number (for anti-gravity) and small (otherwise space would be curved instead of flat.)

In the units where the calculated value of Λ has the value 1, the approximate experimental value of Λ is about 10-120 , or:


The precise value is not relevant, only that it is many, many orders of magnitude smaller than the theoretical value.

So now we see the fine tuning problem. In a nutshell:

How do we get from:

     Λ = 1.0


     Λ = 0.000…..000001

(120 zeroes) without stopping at the unacceptable

     Λ = 0.000…..000002

or proceeding all the way to the unacceptable

     Λ = 0.0

(The actual upper bound is considerably less than twice the experimental value, and the lower bound is not all the way to zero—but that represents a secondary "normal" type of fine tuning.)

The fine tuning of the cosmological constant stems from the fact that there is no known way to reduce the theoretical value by 120 orders of magnitude, especially when it has to end up bigger than zero.

In the words of Lawrence Krauss, one of the chief proponents of the cosmological constant:

Our current understanding of gravity and quantum mechanics says that empty space should have about 120 orders of magnitude more energy than the amount we measure it to have. That is 1 with 120 zeroes after it! How to reduce the amount it has by such a huge magnitude, without making it precisely zero, is a complete mystery. Among physicists, this is considered the worst fine-tuning problem in physics.—Lawrence Krauss, Cosmologist, Sci. Am., Aug. 2004, pp. 83-84.
Krauss, an atheist, characterizes the cosmological constant fine tuning as the "worst" in physics.

I'm inclined to the opposite view. This is the best fine tuning problem. I find it interesting on two fronts. Like any physicist, I love a good conundrum, and I support the efforts of those who search for an explanation for this extreme fine tuning. At the same time, I enjoy the theological implications of physical constant that, were it not 120 orders of magnitude smaller than expected, life could not exist.

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