Ineffective Theory

The Weakness of Anthropic Arguments

Physicists are often bothered by the question “why do fundamental physical constants have the values they do?” Sometimes this concern can be answered by “well it had to take some value”, but not always. Seeking explanations for patterns in what appear to be fundamental constants is a historically successful way to probe for the next undiscovered piece of physics.

The anthropic principle attempts to answer that sort of question. Crudely, an anthropic argument is one taking the form:

The universe is the way it is because if it weren’t, we wouldn’t be here to discuss the issue.

It shouldn’t surprise you to learn that most physicists are, at the very least, a little uncomfortable with this form of argument. The best pro-anthropic-argument summary I know of is frequently given by Nima Arkani-Hamed. Unfortunately I cannot find a video, so my own thoroughly inferior retelling will have to do:

Suppose you walk into a room and see a table. On the table is a pencil, balanced perfectly on its tip. This is unlikely, to say the least. It needs explanation. The first thing to do is look for a string holding it up, or some glue on the tip, or the like. You check, and there’s no such mechanism. The next thing to do is look around — are there thousands of other pencils, lying normally on the table and the floor? If so, then the balancing pencil may reasonably be called coincidence. Alas, there are none.

There’s one last thing to do, to explain the magic pencil: look under the table. Is there a bomb, rigged to explode the moment the pencil falls over? Step outside: do you see the remains of thousands of detonated houses? If so, then it may be correct to say “the pencil was standing because, were it any other way, we would not have been in that room”.

That last check is what an anthropic argument is all about. We can’t actually look for other rooms, destroyed by bombs (that would be called “the multiverse”), but we can at least try and look for the bomb.

The problem is, what qualifies as a bomb? The canonical example: if the cosmological constant were larger by a factor of say, \(10^{100}\), the universe would have promptly blown itself apart. I wouldn’t be here to write this, you wouldn’t be here to read it. Surely we should not be surprised that the cosmological constant is not, in fact, so large.

Does that still make you uncomfortable? Perhaps it should. This type of argument is very slippery (like a slope). Thinking along the lines of the butterfly effect, it’s clear that even a one-part-in-\(10^{10}\) change in the fine structure constant would build up dramatic differences in the evolution and course of life on Earth. In this universe, where \(\alpha \approx 0.007297352569\), you’re reading an article about the anthropic principle; in the universe where \(\alpha \approx 0.007297352570\), at the very least, it’s reasonable to guess that you would not be. (Good news: in that universe, you’re a billionaire playboy philanthropist!) Does this explain (to high precision) the value of the fine structure constant? After all, were the fine structure constant different by even \(10^{-10}\), you would not be considering the question.

This has the basic structure of an anthropic argument, but there’s clearly something wrong with it. In that alternate universe, there are other people who are considering the question “why does \(\alpha\) have that value?” The puzzle would still exist, even if you and I specifically have no interest.

Let’s consider, then, a universe where \(\alpha\) is different by a full one part in a million. Chemical and nuclear physics don’t look substantially different, but again, the butterfly effect suggests that we should expect large differences in the situation on Earth. Suppose intelligent life exists on Earth, but not in anything remotely resembling human form. Now, it’s true that “there are no humans considering the question”. But again, there are beings on this planet considering the question. Shouldn’t that be enough?

Suppose \(\alpha\) were different by one part in one hundred thousand. Now there’s no intelligent life on Earth at all — instead, intelligent life (tripedal, if you were wondering) evolves on Alpha Centauri! Questions of fine tuning are not considered anywhere in our solar system, but there are intelligent beings in the galaxy considering the question. It’s entirely accurate to say “were \(\alpha\) different by one part in \(10^5\), we would not be here to discuss these questions”, but someone would be somewhere, so that doesn’t seem like much of an explanation.

As far as I can tell, the best prototype for a good anthropic argument is:

You have asked why proposition \(P\) (which you find a priori surprising) should be true in our universe. You are able to ask this question in part because \(P\) is true. Were \(P\) false, you would not be able to ask such a question. In fact, were \(P\) false, intelligent beings would not exist at all. Therefore, questions such as “why \(P\)” or “why not \(P\)” would never be expressed. Since questions like “what should be my prior probability of \(P\)” require \(P\) to be true in order to be asked, the answer can only be “your prior should be near \(1\)”. Therefore \(P\) is not, in fact, a priori surprising.

The problem is, this anthropic principle is extremely weak. One proposed use of the anthropic principle is to explain the fine structure constant. Suppose the fine structure constant were in fact 10% different — enough to prevent stellar fusion from producing carbon. This would prevent carbon-based life from existing, sure; but would it prevent intelligent life from existing? Perhaps the question “why is \(\alpha\) that particular value” could still be asked! It’s hard to know, without an unprecedentedly high-fidelity simulation of an alternate universe with \(\alpha = 0.01\). That simulation isn’t coming soon.

The book Dragon’s Egg is based around intelligent life living in the crust of a neutron star. The existence of such life certainly can’t be ruled out with our current understanding of the physics of dense matter. That’s a very different environment than our own; for starters, the strong surface gravity and magnetic field deform atoms by as much as a substantial change to the fine structure constant. If the anthropic principle can’t “explain why” we don’t live on the surface of a neutron star, then it certainly can’t account for a few percentage points in the fine structure constant.

This isn’t just yet another case of “we suck at creating efficient first-principles simulations”, either. One of the most famous stylized facts about cellular automata is that if you sneeze at them, they become Turing-complete. (This isn’t really a special fact about cellular automata, just a reflection of the fact that systems that support complex dynamics tend to also support universal computation.) A Turing-complete cellular automaton can simulate any classical process, and therefore displays phenomena like self-reproducing organisms. Moreover, a Turing-complete cellular automaton can support any intelligence exhibited by a computer. In principle (although of course this is too expensive to have been directly demonstrated) a cellular automaton like Conway’s, beginning from a random position, ought to eventually evolve various levels of intelligence — intelligence is evolutionarily favorable in our world, and ought to be in others as well. So, shouldn’t such automata be capable of asking the question?

(In the case of Conway’s game, I guess the question is “why is the grid rectangular instead of hexagonal?”)

The framework of modern fundamental physics is slightly more complicated than “it’s a cellular automaton” (this is only slightly controversial), but the intuition gained from cellular automata is sticky: even large modifications to physical laws shouldn’t prevent intelligent structures from forming. This is the fundamental weakness of anthropic arguments. A properly formed anthropic argument should be based on an inability for intelligence to form, but intelligence is quite resilient. Almost any non-trivial universe can support intelligent life which will, inevitably, ask the question.

In a few cases, this issue may be circumvented: if the cosmological constant was too small/large, the universe would have collapsed/blown itself to smithereens before having a chance to develop anything resembling intelligence. This is largely independent of the other physical laws. That requirement is not strong enough to remove fine-tuning issues with the cosmological constant, and it certainly provides nothing resembling an explanation for the fine structure constant or any other part of the standard model.

I don’t think this weakness is repairable. Intelligent life is “existentially resilient”. The particular fundamental constants that describe the universe are unlikely to be the only ones that would allow someone to complain about fine-tuning and speculate about anthropic arguments.