2008년 2월 22일 금요일

Universe

An innocent-looking exercise in an English writing textbook asks, "Does the universe have an outer edge?". "Such question is meaningless", I instinctively reply. "You are being philosophical" -- the instructor seems to be surprised.

I wasn't being philosophical. By definition, the universe includes all things that exist. There is nothing outside it. Since there is nothing outside, there can't be an outer edge or an inner edge that exists between the inside and the outside.

This seemingly vacuous wordplay actually poses a serious problem in physics. To see why, we need to discuss the interpretations of quantum mechanics.

Digression. The statement, "there is nothing outside the universe", reminds me of the church doctrine, "extra ecclessiam nulla salus", which means "outside the church there is no salvation". As they say, whatever is said in Latin sounds profound. I wonder what would be Latin translation of the statement?

In the book Three Roads to Quantum Gravity, the physicist Lee Smolin includes the statement as one of his four "points of departure". This 2001 book was finally translated into Korean in 2007. The book is accessible yet rich in deep insights; I recommend it. The following discussion draws heavily from the book. End digression.

Quantum mechanics is an extremely successful theory of physics. The theory lets us calculate the probabilities of measurements. For example, one can calculate the probability of finding an electron at a certain distance from a nucleus. But we can't be sure whether we will find an electron or not.

However, when we actually look for the electron -- in other words, when we perform a measurement -- we either find it, or we don't. And after the measurement, any further measurements are consistent with the electron being at the place it was found, not with the probability to find the electron we calculated. It seems clear that the measurement changed "something", but what something is is not clear. This is called the measurement problem.

The Copenhagen interpretation (well, one of Copenhagen interpretations -- there are many variants) says that the probability distribution represents an observer's knowledge about the system. The wave function, a mathematical tool which gives the probability distribution, describes the system. The wave function is not "real", and when the measurement is performed, the wave function "collapses", and the observer is informed.

Now according to the big bang theory, the universe was once small. There must have been time when the universe was so small that quantum effects were significant. The study of such effects are called quantum cosmology.

If we are to accept the Copenhagen interpretation of quantum mechanics, we need to think about the "observer" of this early universe. But since there is nothing outside the universe, this observer must be the part of the universe, not external to it. Doesn't this sound strange and difficult to you?

If you do you are not alone. Hugh Everett proposed that it's the wave function that is real, and there is no collapse after all. The wave function of the entire universe, which is all there is, evolves in a completely deterministic manner according to the law of quantum mechanics. So when the scientist observes an electron that had 80% chance of being there, it's not that the electron changed to 100% being there. Rather, the wave function describing the scientist evolved to the wave function which describes 80% chance of the scientist-who-found-electron and 20% chance of the scientist-who-did-not-find-electron. Bryce DeWitt later named this "many-worlds interpretation", and the name stuck.

Many-worlds interpretation implies that all possible universes should "exist", since all possible universes have non-zero probability and the universal wave function describes such universes. Thus in some universes I have already written this article yesterday and in other universes this article is never written.

Carried to the extreme, consider a person in front of a gun which fires when a radioactive atom decays. A radioactive atom has 50-50 chance of decaying in its half-life. After the half-life elapses, the person is alive in half of universes. But no matter how long he sits in front of a gun, there is non-zero possibility that the atom has not decayed yet. So in some universes he never dies.

Let's wrap up with a little anecdote. Hugh Everett wrote his thesis The Theory of the Universal Wave Function for his Ph.D. For more than a decade, few people paid attention. Disappointed, he directed his talent to applied mathematics of operation research, and earned lots of fortune. Still he believed in quantum immortality, that he will live forever in some universes; but he died in this universe. His daughter committed suicide, before which she said that she was going to a parallel universe, to be with her father.

Reading what I wrote so far, I guess I was being philosophical after all. But it's hard to avoid being philosophical when you discuss the universe.

댓글 1개:

James :

Sanghyeon,
I am fascinated by this idea of quantum immortality that you touch upon in your post. Could you describe that in a little more detail for me?

I am curious if the theory encompass the possibility of immortality outside the contrived circumstances of being at the mercy of a decaying atom. Does this many-worlds theory suggest that there is a non-zero chance of the existence of universes where people simply do not grow old and die?

James