Commentary: String theory's latest folly

  • 29 March 2008
  • From New Scientist Print Edition. 
  • Lawrence Krauss


THOMAS AQUINAS may never have actually wondered how many angels can dance on the head of a pin, but his tortured musings about metaphysical issues associated with the non-corporeality of angels (and the related issue of whether there is excrement in heaven) stretched the limits of reasonable rational inquiry so far that later scholars invented the phrase to mock him.

My thoughts turned to Aquinas last week as I sat through a lengthy seminar on the subject of Boltzmann brains. The speaker decided his ruminations were so important that he needed 90 minutes rather than the customary hour. To my surprise, many in the room seemed to agree with him.

Before I discuss the topic being debated in this particular ivory tower, let me recap what Boltzmann brains are, and why some string theorists in particular have become fixated by them. Both string theory and inflationary cosmology suggest that our universe, rather than being unique, may be part of a larger structure. Inflation suggests that there may be other three-dimensional universes causally disconnected from our own, while string theory implies the existence of higher-dimensional space. Putting these together, some theorists have wondered if we might explain various features of our universe by the use of the so-called anthropic argument.

This runs as follows. If there are many universes each with different values of some parameter (such as the amount of dark energy), and if life like us can only exist in universes in which the quantity has the value it has, then the value we measure isn't surprising. As several physicists, including myself, have recently shown, the validity of the anthropic principle rests on the assumption that humans are typical life forms.

It has recently been argued that if our universe's accelerating expansion goes on forever, then ultimately random thermal fluctuations will spontaneously produce arbitrarily complicated life forms, just as a monkey playing a piano for an infinite time will eventually play all of Beethoven's sonatas.

These thermal fluctuations have been called Boltzmann brains after Ludwig Boltzmann, the Austrian physicist who developed what is now called statistical mechanics, an idea essential to understanding the thermal behaviour of macroscopic systems. The problem is that statistical arguments suggest that in long-lived universes, far more Boltzmann-brain consciousnesses will develop than intelligences like our own, which have evolved over billions of years. That would mean we are far from typical, so anthropic explanations of our universe fall by the wayside.

Some theorists have therefore tried to develop constraints that would force all inflating universes like our own to decay well before Boltzmann brains can infect them. The bad news here is that in this case our universe must be unstable, and heading for a catastrophic end. But at least anthropic arguments from string theory would not be undermined. You can decide for yourself which you would prefer.

Which brings us to the seminar I had to endure. To calculate how fast various string theory vacuums might need to decay, the audience and speaker discussed whether an isolated consciousness like our own could be imagined to exist without any support system, or whether one has to posit complex systems like galaxies in which to house it. The difference implies a change of a factor in what is essentially a probability estimate from exp(1035) to exp(1070). This is a change of 35 orders of magnitude, not in the probability but in the exponent of the probability!

If debating angels dancing on pins marked the intellectual low point of medieval theology, then we may similarly question the merits of debating problems that require hand-waving arguments involving unknown quantities that differ by billions and billions of orders of magnitude. Let's focus on other issues, at least until better theories come along.

These are unknown quantities that differ by billions of orders of magnitude

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From issue 2649 of New Scientist magazine, 29 March 2008, page 46