Commentary

Scientific Shock and Awe

When I was an undergraduate in physics at the University of Notre Dame, students in the School of Science published a campus science magazine. One article from that magazine that has always stayed with me was a peculiar article on the uncertainty principle of quantum mechanics.¹ This article claimed that for just an instance there could be a battleship on the campus's South Quad lawn.

I'm surprised at how often I run across peculiar articles like this in the popular press written by professors of physics and astronomy. Just last week I found such an article by professor Michio Kaku of the City University of New York on the editorial page of the September 2^nd issue Wall Street Journal. It argued that the universe could be nothing more than data on a supreme being's compact disk.

Now, the idea that the universe could be a computer simulation probably pops into the mind of every physicist who ever simulated a physics problem on a computer, and after the movie The Matrix, which is acknowledged in the article, there is probably no one on the planet who is not familiar with this idea. What is striking about the article is the author's scattershot use of physics in exploring this idea.

The author begins with a bait-and-switch. He first has us imagine that the universe is itself just a collection of information: “Physicist Jacob Bekenstein has claimed that our universe might be an illusion, perhaps consisting of 10¹⁰⁰ bits of information that can be stored on a disk.” Kaku then begins calculating the maximum amount of information that can be stored in a given amount of space.

But how can we even think of such a possibility in terms of known physics? Kaku's conjecture that our reality is actually a computer simulation implies that a part of the universe affects us without being unknowable to us. It is in this part of the universe that a computer would exist and simulate our reality. But why in this fanciful speculation would the physics of the unknowable universe be the same as our observable universe? We cannot know the larger universe conjectured by Kaku, so any discussion about the simulation of our reality by a supreme being that hinges on the physics of the observable universe is worthless. Perhaps recognizing this, Kaku perpetrates the switch, turning the discussion to our own simulation of reality.

Three reasonable questions can be asked about this: can a computer precisely simulate reality; how much memory is required by a computer to do this; and can a computer with this amount of memory be constructed? Kaku does not address this in a meaningful way. His discussion is instead a disconnected set of ideas and jargon from ancient philosophy and the most speculative realms of physics. First he invokes Zeno's paradox: to reach a given point, one must first move half that distance to the point; but because one must still move halfway to the point with each motion, one never reaches the point. From Zeno's paradox, he concludes “So the universe cannot be places on a CD, and you cannot even hit the ‘play’ button.&rdquo But then he states that Newton resolved the paradox with calculus, so that now the “play” button can be pushed, but the universe cannot be simulated. But why bring up Zeno's Paradox, if it is irrelevant to the modeling of the universe?

Kaku's reason for not being able to truly simulate reality is incomplete. He points to our inability to model every molecule in a system because of the large number of molecules in any macroscopic system. But a more important obstacle is that our fundmental equations of physics use real numbers, while computers use truncated numbers. Even the motion of a dozen molecules cannot be precisely simulated because the truncation of numbers in a simulation and the unavoidable use of finite time steps introduce errors into the simulation results. The author cannot dwell on this point, because he has something more exotic than computer round-off errors to discuss: black holes.

Kaku wants to use black holes as a storage device in a computer that truly simulates reality, so he ignores the more mundane truncation problem. If enough information can be stored on the black hole's event horizon, then information about every molecule in Earth can be stored on the computer. Kaku cites the calculation by Bekenstein, who with Stephen Hawking developed the theory of black hole evaporation, that a black hole with a 1 centimeter diameter can store 10⁶⁶ bits of information on the event horizon, and that the number of black holes within the observable universe is sufficient to store 10¹⁰⁰ bits. Is this sufficient? Kaku doesn't say, because he is off to the next big thing: superstring theory, a speculative theory that many hope can describe all physics. And what does superstring theory say about simulating the universe on computer? Kaku claims that it gives the same value for the amount of data that can be stored on a black hole's event horizon as was calculated by Bekenstein, and, by the way, the universe may be a hologram.

So how do you store something on an event horizon? Why, you throw a book onto it! “If you threw a book into a black hole, its information was somehow encoded on the surface. (You really can judge a book by its cover!)” One problem with all of this discussion is that it treats the event horizon as a membrane, when instead it is the points in space where light can no longer escape to an outside observer. A person falling through the event horizon of a black hole would see nothing special, and there is no local experiment he can perform to show that he is at the event horizon.

After this speculative sprint, what does Kaku finally conclude? He concludes out of the blue that we cannot simulate the future on a computer because of the uncertainty principle, but we may be able to revisit the past. This final conclusion is wrong, because the uncertainty principle applies just as much to calculating the past as it does to calculating the future. The uncertainty principle is a statement about the probabilistic nature of quantum mechanics, and many different past states can give rise to our present state.

This column takes a shock and awe approach to popular physics; it substitutes flash for understanding. It reminds me of the dreadful sci-fi movie “Independence Day,” where miles-wide flying saucers float above major cities for no discernible reason other than that the images are cool. Likewise in this article, Zeno's paradox, superstring theory, and black holes appear in the context of computer simulations of the universe for no other reason than that they are fanciful. The most beautiful aspect of science, that we can understand our complex reality in terms of a small number of simple principles, is lost in a flurry of random and exotic images.